Hello,

I often notice in video games and animated films the animations behave a lot like real people and not a mesh.
If you ever done amateur mesh rigging and animating, then you know most of the movments yo can do will look terrible if they exceed that meshes limits, however in these animation the human body actually looks like it functions.
My question is, what exactly do they do to make their meshes not behave like a mesh but like a body with tensing muscles and everything.

They use live actors. Many games have almost as much production as a major movie release. They use sensors on the body of the actor / actress and gather the information to put into the computer to compile a figure for movement. One example that comes to mind is in the movie The Lion King and when the bison are charging over the hill what your actually seeing is digitized ants that have been overlayed and animated.