So a bunch of people get together and have this brilliant idea for a CG Animation project. It all starts with a script writer, a director, a producer and a few concept designers.

Script Writer
The script writer is the person who obviously writes the basic idea of the story. Script writers are hired by contract and for a period of time till the script is more or less 'production ready' (meaning its gone through discussions with the producers, creators and they've checked their budget and everything is cool) However this doesn't mean that the script doesn't change during the course of production. Its only a basic outline and the director has the liberty to tweak some dialog and scenes to fit certain constraints or his vision of the story.

The Director
The director is pretty much the storytelling god. He's like the Dungeon Master of a D&D game. He is the guy who decides on how he wants to tell the story, the certain look and feel of the show and how it starts and ends. He works along side the Producer who helps him make sure there's money for the project, the right people are hired for the job and makes sure the project finishes on time. The director has to know EVERYTHING about film production and should have firm vision of what he wants, what he likes and doesn't like.

The Producer
The producer is the person who gets the story made. They look at the script, think about how much its going to cost, who they're going to hire to envision the story and make sure the show gets done. They are also responsible for finding funding for the project and will work hand in hand with the director to find the best people possible for the job.

Concept Designers
Concept Designers are the guys who turn the words on the script into beautiful drawings to envision what the director has mind for the story. They do everything from environments, characters, props and vehicles. Concept Designers are hired on a contract basis and design stuff with the intention that a 3D modeller will pick up their designs and build them in virtual space. Concept Designers are akin to mini architects, interior designers,product designers and fashion designers as their design blue prints will be referred to by texture artists, riggers and modelers. Some very clever concept artists also do Marquettes - sculpted forms of the key characters in the show for reference to the modelers, to conduct early lighting tests etc.

So once the story has been pinned down, producer's happy, director has been found, concept art has wowed people. Production can officially begin on the project.

3D Modelers
These guys are your 3D sculptors and builders. Once the concept designers are ready with the final designs of the characters/ props / environments etc. The 3D modeler gets to work at converting the 2D designs into 3D objects. They usually start with proxy low-resolution stuff first to hand to the pre-viz artists (fancier name for story board artists) than move on to the medium resolution stuff (used for middle ground stuff and close ups) and high resolution stuff (used for extreme close ups that require a lot of detail)

In some cases, modelers double up as texture artists who add paint and color to their gray models to bring them to life.

Nowadays, the industry standard in modeling is Zbrush for organic modeling, Maya for 3D CG animation and 3D Max for game modeling.

Texture Artists
Without textures, a model is a gray form. Texture artists are the painters who bring the model to life with color and texture. Texture artists are usually highly skilled painters (usually in Photoshop / Painter) and are aware of how to use 3D programs to apply and adjust textures for models.

Riggers
Riggers are the 'renaissance men' of the CG Anim world. They add bones and points of articulation in models that are meant to move and function. It's like the guys who figure out how to make your action figure twist and bend its arms and legs. That's pretty much what riggers do. Note that not all models are rigged the same way. If a character is meant to do something outrageous in an action scene, it has to be rigged with extra bones and joins for him to move a certain way, rather than the character who's just going to be walking and talking. Riggers may be required to do several versions of a character / object depending on its purpose in the show.  

So with all the sets, props, characters all rigged and in place, its time for the pre-viz artists and directors to get their stuff going

Pre-viz Artists
In the old days, these guys were called 'story board artists'. They're kind of like comic book artists who draw sequences of images, show which way cameras are moving and concentrate on telling the story visually.

Nowadays, this task is done in 3D to save time and help the director envision better what the story looks like in front of a camera.

Pre-viz artists grab proxy assets from the modelers and start telling the story in basic poses with characters sliding here and there just to get a sense of how the story is to be told. Sure, previz doesn't look pretty and the voices talking are temporary but it gives a good general idea to the director of how the story will look like.

Editors cut together the reel out of all these shots and once the reel is locked down, director's happy with the revisions, final dialogue is recorded by the voice actors, the real animation of the show gets underway.

Layout
Because Pre-viz is a rough process, sometimes camera moves aren't smoothed or corrected before it goes to production. The Layout team are like virtual camera men who ensure that 3D shots are cleaned up, cameras are smoothed out, things are all neat and tidy before Animation can begin with their shots. Layout guys are more like technical artists who should know and understand how cameras move and track. Once all that is cleaned up and the director acknowledges that the camera moves are all good. Animation can begin.

Animation
Everyone pretty much knows what an animator does: he brings the models to life. He makes them act, react, emote and such. Animators are the masters of movement and are very good at re-creating movement and acting. Animators are also very hard workers because they have to animate every shot in the entire show, also, the process of animation takes quite a fair bit of time and tweaking. Animators animate with med res models so that its faster and easier to work with rather than the hi-res stuff. So once the director is happy with the way everything has turned out in animation, it goes to hair /cloth sim.

Hair / Cloth sim.
Hair / Cloth sim guys aka Creature Technical Directors rig up cloth on selected characters (things with flowing bits like flaps and skirts, jackets and robes) and animate how cloth rises and falls when characters move. In some cases, these guys also animate things like hair, fur, ropes and bendy stretchy things. Cloth sim artists study the science of soft objects falling, the way certain fabric move and folds and the movement of hair and fur. When those are all good to go, all these shots are checked in the Checkpass department.

Checkpass
Checkpass are a team of assistant tech directors and tech directors who make sure everything looks ok in every shot. Character arms are not passing through legs, things not chopping off etc. They run a script that assigns a different color to all the 3D shapes in the shot and make sure they don't intersect, cross or go through each other. ATDs and TDs are technical people and are the fix-it people who help people across various departments if its software related (stuff can't open, things not loading correctly etc) These guys are usually computer science people and know the particular 3D program inside out and have scripting knowledge.

Effects
Need stuff to explode? Dust to fall on the floor? Mist to drift in the background? Effects people are your men. Effects artists are the mages of the CG animation world. They create fire, rain, mist, dust to fall in shots that require them. Effects people are also animators and are experts in how natural phenomenon should move and react when forces are applied to them. They have a strong understanding of physics and know a bit of scripting and have a good visual eye for how things should look in nature.

Lighting / Compositing
With all the key animation, cloth sim, effects in place, its time to light the scene and finish the visual production of the show. Lighters are the guys who create mood and feel in every shot with directions according to lighting concept paintings (painted by lighting concept artists) Lighters set up their virtual lights in each shot and render out the scene with full textures, hi-res assets and a little extras on the side like composting together background mist etc. Lighters are usually photographers and know how to create mood and tone in their images to create that added dynamism to the show and story.

Editorial / Color Correction / Post-Production / Music etc.
So once the entire visual look of the show is done, it gets sent to editorial for a final trim to make sure it fits into the required time slot etc. Color Correction is done to the reel to make sure color is same across the show or some elements are brought out more etc. Music and sound effects are added to show and viola, the show is finally done, launched, on TV etc.

Also, who gets all this stuff on the road and makes sure everything gets done on time? Production people!

Production Managers
Production managers are the guys who make sure things get done on time and on target. They also look for ways to make things more efficient and do quite a fair bit of scheduling. Production Managers manage things, are concerned with when things get done, how they get done and are all about numbers.

Production Coordinators
They are the tasks masters of a department ensuring things get fixed when they're supposed to, they track where shots are, who's doing them, making sure artists have enough work to do and that overall production keeps going in their department.

Production Assistants / runners
When PCs are too busy to do lesser things like print documents and manage simple tasks, the production assistants are the ones running around and checking on things just in case the PC doesn't have time to. Production Assistants are the basic grunts in the production department and that's how most people get started in the production side of the industry.

Production Accountants / Finance / HR / Recruiting
the background people who work behind the scenes to make sure things are moving smoothly and not impairing the production overall.

And that's pretty much the people involved in the CG Animation industry. Titles vary from company to company but those are the basic jobs involved when a CG animation gets made.