Question

What is the momentum of a physical system

Answer 1

Mathematically? Mass times velocity.
\[\vec{p} = m\vec{v} \]
Equivalently, it's the time-integral of force (in the same way energy is the time integral of power).
\[\Delta\vec{p} = \int^{t_2}_{t_1}\vec{F}~dt\]
if force is constant
\[\Delta\vec{p} = \vec{F}t\]

Answer 2

That helps. I was looking for the definition

Answer 3

It's such a difficult concept to put into words. You can think of it as how "hard" an object is moving or a measure of how difficult it would be to stop. Every single definition always explains it as "mass times velocity".

It's a bit more fundamental than that, though. Particles of light (photons) do not have mass but they have momentum, but you probably don't have to worry about that.