The coordinate system from which an observer takes measurement of events in space and time (classical mechanic) or in spacetime (special and general relativity) is called a frame of reference.

Within the realm of Newtonian mechanics, an inertial frame or inertial reference frame, is one in which Newton's first law of motion is valid.

 Newton's first law:   An object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

So then you might be wondering, when could Newton's first law ever not appear to be true?

Imagine you are on Earth and assume that you could remove both friction and air resistance.
Now hit a ball gently so it moves slowly along a perfectly smooth road with uniform velocity. If we were in a strict inertial frame, the ball would move in a straight line along the road, but it's not the case: due to the Earth's rotation, the ball's path is ever so slightly curved.

This force causing moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the North Hemisphere and to the left in the Southern Hemisphere, known as the Coriolis effect, along with the centrifugal force, is precisely what makes the rotating Earth a non inertial frame. Coriolis effect in an inertial, at rest frame (top) and in a non-inertial, rotating (bottom) frame

More generally, apparent forces which are not caused by any physical interaction but are due to an observer using a non-inertial frame of reference - rotating or accelerating - are known as inertial or fictitious forces.

It leads to our second, more general definition of an inertial frame of reference:

 Inertial frame of reference:   The inertial frame of reference is the one where the fictitious or inertial forces vanish.  In other words, the laws of physics in the inertial frame are simpler because unnecessary forces are not present.

An inertial frame obey the following properties:

1. If you are in an inertial frame and have no communication with the outside world, there is no experiment that will tell you whether your frame is at rest or moving with a uniform velocity: this is known as the Galilean relativity principle.
2. Any frame that moves with constant velocity relative to another inertial frame is itself an inertial frame.
3. Any frame that is accelerating or rotating relative to an inertial frame cannot itself be an inertial frame.