Velocity and acceleration describe the motion of a single object.
Momentum (p) is measured by the product of mass and velocity.
The momentum is directly proportional to an object's velocity, so its vector is along the same direction as the velocity.
That being said, momentum is a way to describe a motion of an object by looking at the product of its mass and velocity.
Momentum shows the level of difficulty in decelerating an object. Or put another way, the "unstoppability" of an object.
Momentum shows the level of difficulty in decelerating an object. An object with large momentum requires a large force to act over a short time to bring it to rest, or it requires a smaller force to act over a larger period of time to bring it to rest.
The change in momentum is equal to the product of force applied and the time over which the force acts.
Change in momentum is called impulse, so this answer is based on the definition of impulse but it does give some meaning to momentum as a quantity.