Box2D was created by Erin Catto and is an open source physics engine for simulating rigid bodies in 2D space. It is written in platform-independent C++ code that has encouraged ports to several frameworks, game engines, and programming languages in general.
You should really check out at least one of the following popular games if you have never seen Box2D in action before: Angry Birds, Limbo, Tiny Wings, and Crayon Physics Deluxe.
Libgdx integrates Box2D, similar to other frameworks, through a thin wrapper API that is congruent with Box2D's original API. This approach makes it pleasantly easy to transfer existing knowledge about Box2D by following tutorials and examples that are not based on Libgdx, and, of course, by using the official Box2D manual.
For more information, check out the official website of Box2D at: http://www.box2d.org/