I’m going to define a mathematical object called a phase space. This is supposed to be a set of observable facts about a physical system (a “phase”); each point might represent a specific position and specific momentum, or it might be something coarser. Informally, we want that if we specify an energy function which only depends on the phase, then we can tell how the phase evolves with time, and this evolution is “reasonable.”

http://sbseminar.wordpress.com/2012/01/09/what-is-a-symplectic-manifold-really/