I use 3ds max in my profession and can give you a brief intro to animation.
Animation in games have a variety of types as gord says, you have hand made animations, MOCAP animations and you have physics based or a mix of all of these
Hand made animations can be as simple as a door opening and closingin a pre defined way to a much more complex scenario but if its hand made then its pre defined it can't be affected. a simple animation that is used a lot is simply to rotate an object on the spot so you can see it from all directions.
MOCAP animation is animation that is recorded, (motion capture) this is how a lot of games do the animations for characters walking, running etc these can also be mixed together in a motion mixer to make a blended animation. imagine a character running and shooting at the same time. these are generally filmed in a mocap studio with a live actor wearing a suit with 3d points on them. these points are then recorded and turned into mocap files that can be used on models to simulate what was recorded
Physics based animations are where you give objects real world properties; mass, elasticity, weight (define gravity) etc etc and then you let them interact with other objects i.e one simple physics based tool i use at work is to simple give a load of objects weight and let them fall to the floor or into a bowl etc. this is really handy as it gives them a realistic look as if they've been dropped without me having to sit there and play with each object one at a time getting them to look perfectly random.
the same applies to games, if you want something to reach realistically you have to make it react to the world realistically. this also makes it slightly out of your control so sometimes hilarious things happen with the physics when it screws up
an animatior himself will take objects made by modellers and then he would give them movement.
a character for example has whats called a RIG this is almost like a skeleton
you can see here a simple rig for a character.
these give the character constraints, for example how much can each bone rotate, move etc.
once you have the rig set up you can set about either importing your mocap information or creating animations by hand.
the subject is much much deeper than i've gone into but hopefully that gives you a brief idea