Topological intuition about a hamiltonian vector field

Question

Could I ask a conceptual question?

If you have a symplectic manifold ($M$, $\omega$) and a real valued function $f : M \to \mathbb{R}$, you can define a hamiltonian vector field $X$ corresponding to $f$ by the following equation;

$$ i_{X}(\omega) = -df $$

Then could you give me a topological intuition about the hamiltonian vector field?

Thanks.