Think of "baking" as you would in real life ... when you "bake" a cake (for example). When baking a cake you first get all the ingredients you need, mix them all together and then for the final step (before it becomes an actual cake) you bake it. Baking it takes all the ingredients and gives you the final product: the cake.

In the gaming world, as Frank pointed out, you can "bake" a lot of things (just like you can bake more than just cakes ). But you first have to put together all of your ingredients. If you want to bake a shadow into a texture (Frank's first explanation) then you will need your texture and your shadow (or a light to cast the shadow). Once you have your "ingredients" you can then bake to get the final results (a single texture that includes light and shadow information).

You mentioned animation. The same would apply. Someone would gather all the ingredients (model, bones, etc) and bake the animation so that you get a final result: a model that is now animated.

Often, for a game model, someone will create a high polygonal model and a low polygonal version as well. The high polygonal model will be used to "bake" a normal map for the low poly model to make it look like it has more detail. The modeler may also bake other maps such as ambient occlusion, bump maps, etc. Depending on the application used, this baking process can be done in one step (provided all the ingredients are there and ready to be used).

So, again, baking, as in the real world of cooking, is putting the ingredients together properly and, as a final step toward the final result, baking those ingredients together to form a single entity (a cake for cooking, a model for a game, etc).