Bullet is a 3D Collision Detection and Rigid Body Dynamics Library. The Library is Open Source and free for commercial use, under the zlib license (more info).
The Bullet physics extension is a Java wrapper for the C++ engine. This page provides information about using that wrapper. For more documentation related to the Bullet engine, please visit bulletphysics.org. Any Bullet questions not related to libGDX specifically can best be asked on their forum.
Practical information and examples on how to use the bullet wrapper can also be found at the Bullet tests.
These tutorials provide an introduction in using the Bullet wrapper: