Question

Why momentum is used and for what purpose?

Answer 1

I believe your questions is "need for momentum or importance of momentum". Before getting into question, let's see what is momentum first.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space.Wikipedia
SI unit: kilogram meter per second kg⋅m/s
Other units: slug⋅ft/s
Common symbols: p, p
Dimension: MLT−1

Momentum is the quantity of motion of a moving body. In a basic sense, the more momentum a moving object has, the harder it is to stop. This is why you see the term used metaphorically like in the example of the sports team. It means the team is on a roll (generally, a winning streak) and is becoming a stronger team for it. The other teams will have a harder time stopping the team gaining momentum.

Now coming to your question, It is important when solving for collisions and explosions. Because momentum is always conserved, given enough information about the path of the object(s) before the collision or explosion, you can predict the resultant path afterwards.

Momentum is a valuable tool for predicting the future of physical systems. It joins the ranks of kinematics, forces, and energies.
As I already said, what sets momentum apart is that it’s a conserved vector quantity. Compare that to energy, which is a conserved scalar, and to forces, which are only conserved locally. Momentum lets us apply the tools of vector algebra to physical systems. It gives us additional insight into how systems evolve.

Hope you understand.