How is a frame of reference used to describe motion

In particle kinematics, we measure the acceleration of the particle. For this, an observer is taken as a reference point. Generally we consider the observer as in origin of a co-ordinate system. The place where observer is placed is known as frame of reference. 
Newton's laws only work in the inertial frame of reference. Inertial frame is a frame of reference whose acceleration is zero. But, if you are observing the motion of an object from non-inertial frame, you need to add and extra force on the system under observation which is known as pseudo force.