Hi, to completely describe a classical mechanical system, you need to do three things:

-Specify a manifold $X$, the phase space. Intuitively this is the space of all possible states of your system.

-Specify a hamilton function $H:X\rightarrow \mathbb{R}$, intuitivly it assigns to each state its energy.

-Specify a symplectic form $\omega$ on $X$. What is $\omega$ intuitively? What kind of information about physics does it capture?