Spherize

What is the Spherize effect? 
Spherize is a deformation effect that simulates a spherical force pushing out from inside a model.  It can be used for things like muscles, joint compensation (like at the elbows of a character), snakes swallowing food, etc.

How it works:
The tool that Spherize uses is a Null.  So when you add Spherize to an object, it will create a null with the effect attached.  You position this null where you want the effect to be, and likewise, it is this null object that you animate if you want to move the effect (see image above).

For more interesting effects, try adjusting the shape using the X, Y, and Z scale, or use multiple spheres.

Extreme Muscle:
The  Scenes\Samples\  folder has a great example of how to use Spherize for muscles.  This scene is a bit complicated, because it was made as a test (by animator Patrick Van Pelt), but you'll quickly see the basic principles involved.

Additional Information:  Spherize block    Spherize Tutorial