Most often, they are polygonal or spline based meshes. For example, an artist will create objects that look like feet, hands, head, torso, hair, clothing, etc. These are then assembled to represent the character. In general, these representations of the human body are called 3-D body models. Body models can be made from scratch in the animation software or they can be purchased.
Many companies sell collections of models and do custom work.
The mesh deformation software is almost always part of the animation package itself. However, many third party mesh deformation plug-ins are available. It is also used to create muscle bulges and clothing movement. Once the skeleton is skinned, the character animation is complete. Other features available in all animation applications can then be used to put the character in any given environment.