Momentum is the tendency for objects at rest to stay at rest, and for objects in motion to stay in motion.
The greater the mass of an object, the greater its resistance to changes in motion. Also, intuitively, the greater the velocity of an object, the greater the momentum it possesses. Therefore, the momentum of an object can be quantified mathematically as p=mv, or as mass x velocity.
The greatest usefulness of the concept of momentum lies in the fact that the total momentum of a system of objects is always conserved, i.e., in isolation the total momentum always stays the same. This knowledge allows the solution of many problems in physics with great elegance. For example, in rocket propulsion; the mass of propellant a rocket carried multiplied by the exhaust velocity of the engine, will be equal to the final forward velocity of the empty rocket multiplied by its empty mass. Without understanding the principle of conservation, finding the final velocity of the rocket would be very puzzling; but applying the simple equation mv = m’v’, and rearranging to v’=mv/m’, finding the velocity becomes a very simple calculation.
The principle of conservation of momentum applies to all states of matter, i.e., solids, liquids, gases, and plasma (and subatomic particles), and with all forms of interaction through all forces, such as gravity, magnetism, direct contact, electrostatic force, etc. etc., so the scope and range of application of this principle is vast. It is easily one of the most important concepts to understand in solving problems involving motion.
The concept of momentum can also be applied to rotating objects, in which case the momentum possessed by such rotating objects is called 'angular momentum'. Angular momentum is also conserved.