Dynamics is a branch of physics that describes how objects move. Dynamic animation uses rules of physics to simulate natural forces. You specify the actions you want the object to take, then let the software figure out how to animate the object.
Dynamic animation lets you create realistic motion that's hard to achieve with traditional keyframe animation. For instance, you can make effects such as tumbling dice, waving flags, and exploding fireworks.
The Maya Dynamics guide, which provides information about creating dynamic simulations in Maya, is available at http://www.autodesk.com/maya-docs-archive.