Newton's laws of motion are three physical laws that, and these three laws together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.We can say that, the first law defines the force qualitatively, the second law gives a quantitative measure of the force, and the third asserts that a single isolated force does not exist. These three laws have been expressed in many different ways.

Newton's First Laws Of Motion

Newton's first law of motion states that in an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a unbalanced force.

In simple words it means that there is a natural tendency of objects to keep on doing what they are doing and all objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain this state of motion.

The first law can be stated mathematically represented as

Consequently,

• when the mass is a non-zero constant
• An object that is at rest will stay at rest unless a force acts upon it.
• An object that is in motion will not change its velocity unless a force acts upon it.

This is also known as the law of inertia. The law of inertia was first formulated by Galileo Galilei for horizontal motion on Earth and was later generalized by René Descartes. Before it had been thought that all horizontal motion required a direct cause, but then Galileo deduced from his experimentation that a body in motion would remain in motion unless a force (such as friction) caused it to come to rest.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The Newton's first law of motion postulates that there is  at least one frame of reference called inertial reference frame,and relative to which the motion of a particle not subject to forces is a straight line at a constant speed. Newton's first law is often referred to as the law of inertia. Thus,we can say that a condition which is necessary for  uniform motion of a particle relative to an inertial reference frame is that the net force acting on it is zero.

Newton's Second Laws Of Motion

Newton's second law of motion states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force.

Everyone unconsiously knows the Second Law. In simple words It means that heavier objects require more force to move the same distance then the force required by the lighter objects to move.And the Second Law gives us an exact relationship between force, mass, and acceleration. The mathematical equation the second law ca be represented by:

or
FORCE = MASS Times ACCELERATION
Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. Acording to the Newton's second law motion that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased,correspondingly the acceleration of the object is also increased. As the mass of an object is increased, the acceleration of the object is decreased.

Newton’s second law of motion is a quantitative description of the changes that a force can produce on a body which is in motion. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum, or its direction, or both. Newton’s second law is one of the most important law in all of physics. For a body whose mass m is constant, it can be written in the form F = ma, where F (force) and a (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it.

Newton's Third Laws Of Motion

Newton's third law of motion states that when one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude but opposite in direction on the first body.

It means that for every action there is an equal and opposite reaction.

The third law states that all forces between two objects in a region exist in equal magnitude but opposite direction,if one object A exerts a force F_A on a second object B, then B simultaneously exerts a force F_B on A, and the two forces are equal in magnitude but opposite in direction: F_A = −F_B.
The Newton's third law of motion means that all the applied forces are interactions between different bodies, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces acting on the bodies is determined entirely by one of the two bodies, say Body A; the force exerted by Body A on Body B is called the "action", and the force exerted by Body B on Body A is called the "reaction". This law on motion is sometimes referred to as the action-reaction law, with F_A called the "action" and F_B the "reaction".
In other situations the magnitude and directions of the forces acting on a body are determined jointly by both bodies and it is not necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the action and which is called reaction; both forces are part of a single interaction, and neither force exists without the other.

For even better understanding you can refer to the videos above.