Momentum is a scientific term dericed from various observations about the nature to describe the nature of force .
Imagine space where there is no external force acting on a body(no gravitational ,electrostatic ,magnetic...forces).
If we initiate a motion by a small force ,then remove the force the body will move with constant motion after the force applied .It was found that ,if an cololision with another body ,the impact increases if mass was kept constant and when the velocity was increased each time in the experiment . the impact increases if the velocity was kept constant and when mass of the body was increased each time. so, a term momentum has to derived to explain this . The impact or force that was applied also depended on this change in momentum.
the momentum depended linearly on both mass velocity.so from this it derived to be a product of mass and velocity.momentum is vector as velocity is a vector .
the momentum changes when the velocity vector changes such as when velocity of ball changes while playing cricket or direction of velocity changes for a ball in horizontal circular motion.
An example for momentum change when for mass change is rockets . the rockets can expend the mass with constant velocity , to use this force to thrust into the space.