Newton's third law of motion states as follows:

To every action there is an equal and opposite reaction.

The reality of Newton's third law of motion can be seen in the following instances:

• An object placed on a table. There are two forces acting in opposite direction on the object.

One, is the Action of the object on the table. This is the weight of the object pressing down on the table.

The other is the Reaction of the table on the object. This force acts vertically upward on the object.

These two forces, i.e., the Action and the Reaction forces are both equal in magnitude, but act in opposite direction.

• A moving ball that hits a stationary one. If a moving ball, A makes contact with another, B, which is at rest, there will also be two opposite and equal forces at play.

One is the force of A on B, which is the Action, and the other is the Reaction of B on A, which is equal in magnitude to A, but in opposite direction.

• When someone fires a gun. As the bullet is fired, the person would experience a backward force as the gun recoils.

The force that acts and moves the bullet forward is the Action, while the backward recoil force of the gun is the Reaction.

Both forces are equal in magnitude and move in opposite direction.

Something to note:

For the fact that force is proportional to rate of change in momentum, as expressed in Newton's Second Law Of Motion, it therefore follows that the momentum of the bullet is equal to the momentum of the gun.

Therefore, if M is the mass of the gun with velocity V backward, and m is the mass of the bullet with velocity v forward, a mathematical equation can be established:

MV = mv

Application Of Newton's Third Law Of Motion -  the movement of jet planes and rockets

A very important practical application of Newton's third law of motion is the transportation of jet planes and rockets.

The movement of both planes and rockets is made possible by large mass of hot gases gushing out from the nozzle behind them.

As the gases pump out with enormous momentum, considering the huge velocity and mass per second of the gases, there is also an equal momentum in the opposite direction, which thrust the jet plane or rocket forward at great speed.

A rocket propelled forward by the momentum its burning fuel gas generates  - the burning gas gushes out downwards.
(Picture from http://www.defenseindustrydaily.com

See calculation of force based on Newton's third law of motion here.