Newton’s first law says that if the sum of all the forces acting on a particle is zero then the particle remains at rest or moves with constant velocity i.e. acceleration of that particle is zero.
Have you observed hanging hand grips inside a bus or train compartment?
Its weight is acting vertically downwards and the tension in its strap is pulling it upwards with an equal and opposite force. So the hand grip should be in stable condition when there is no external force visible, within the framework of the compartment.
But we often see it swaying when the train moves.
We understand that Newton’s first law is to be checked after we take a frame of reference and then find out the acting forces on a body or a system present within that framework and the presence of acceleration in it with respect to that framework. But there are even some frameworks where this law is not valid.
So what type of framework is only valid here?
We can take the earth as a valid framework as its moving uniformly. With respect to it(taking it static) we consider a tree or house on it as a static object. We call this frame of earth as an Inertial framework.
Similarly a uniformly moving train is again a valid framework with respect to the inertial framework of earth. So we can say that all frames moving uniformly with respect to an Inertial frame are inertial themselves.
So to conclude, an inertial frame of reference is a framework in which Newton’s first law is valid. example: a uniformly moving vehicle
A frame in which this law doesn’t hold good is called Non-inertial frame of reference. example: a train moving with acceleration.