We just had the definition of a symplectic structure on a vector bundle in the lecture and I am having trouble understanding it
Definition: Let $\pi : E \to M$ be a smooth vector bundle. Then a symplectic structure on E is a smooth section $\omega \in \Gamma( \bigwedge^2 E^*)$ such that $\forall x \in M$ the value $\omega(x) = \omega_x$ is a symplectic form on $E_x = \pi^{-1}(x)$.
I know in general what vector bundles and smooth sections are. But I don't quite understand the bundle structure on $\bigwedge^2 E^*$ or the projection map there. And consequently I don't understand why as a smooth section $\omega$ is a collection of symplectic forms on the fibers.
Thanks in advance for any help !