In Newtonian physics, inertial frames are frames that are in uniform motion w.r.t a selected absolute frame of "fixed stars" (we're talking Newton here, so we can have absolute frames). Non inertial frames are frames with acceleration involved (like the rotating frame we have on earth).
In accelerating frames, Newton's first law can be seen as obviously invalid. An object at rest in an inertial frame can be seen to accelerate in a non-inertial frame, even though there's no force acting on them!
To make the laws come out right, you have to add "pseudo-forces" to the system (which don't really exist), to account for the non-inertiality. One example of a pseudo-force is the Coriolis force on Earth, which accounts for the fact that we're on a spherical rotating frame of reference.
Thus:
- The 1st law does not hold in non-inertial frames
- The 2nd law can be made to hold by adding "pseudo-forces" into the picture
- The 3rd law does not apply to pseudo-forces
