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Inertial frame of reference is frame of reference in which Newton's first law remains true.
Lets say someone is driving a car and you are the passenger. From your point of view in the vehicle, you and the driver of the car are sitting still. However, to a bystander standing still outside the vehicle, you and the driver appear to be moving. We can call these two points of view two different frames of reference. In physics, we classify frames of reference by two main types: inertial and non-inertial.
Inertia is the property of matter in which an object that is at rest wants to remain at rest, and an object that is moving wants to remain moving in a straight line unless another force acts upon it. Likewise, an inertial frame of reference is a reference frame in which an object stays either at rest or at a constant velocity unless another force acts upon it.
When a body does not seem to be acting in accordance with inertia, it is in a non-inertial frame of reference. In other words, a non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame.
Let's continue with the earlier example. Let's imagine the car with you and the driver is a limousine and the road is very smooth so you have no way of knowing if the car is moving or stationary. In fact, to you, all that matters is that you both are sitting in the car. The bystander outside the vehicle will always be in an inertial frame of reference since he or she is standing still, i.e., at rest. For you, it depends on the vehicle's movement. Let's assume the vehicle is moving in a straight line. If the vehicle is not accelerating, then you and the driver are also in an inertial frame of reference. This is because no acceleration means your velocity is constant. If the vehicle begins accelerating, you and the driver are now in a non-inertial frame of reference.
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