Yeah, "inertial frame" is the key term, but the philosophical question that I find a bit difficult is the following. Imagine a single space station in an otherwise empty universe. How could you tell whether the station rotates or not? You can claim that it rotates, if and only if all objects on board feel the effect of this centripetal force. Or more generally, you can say that is undergoes an acceleration, if the passengers feel the resulting forces. But, like motion, acceleration is also defined with respect to a frame of reference. Without a single frame of reference other than those attached to the station itself you are lost. And it is not clear what happens, if your thrusters change the of spin the station. Will everybody feel a change in the artificial gravity, if you still don't know, whether you rotate or not?
Sir Isaac solved the problem by postulating an "absolute space", but this created other problems, and lead, eventually, first to the
special and later to the general theory of relativity (both by Einstein), the first got rid of the need for a frame of reference to define motion, and the latter (according to my feeble understanding) the need for a frame of reference to define acceleration (and hence also inertial frame) building on the observation that the effects of gravity and acceleration are locally indistuingishable.
I am under the impression (but also prepared to be wrong) that the distant stars do affect, and essentially give that frame of reference. The mechanism is vaguely similar to the way the nature balances its books, when there are moving electrical charges.
The laws of electromagnetism are immune to motion at constant speed. Yet moving charges create different forces (magnetic as opposed to the Coulomb force) that exactly compensate for the difference that would otherwise result from shifting to a stationary coordinate system to one that moves (at constant speed) together with the charged particle. Similarly, if your coordinate system is not inertial, e.g. it rotates with respect to the distant stars, then those distant stars would move at huge velocities w.r.t. your frame of reference, and then affect you by... making you feel an artificial gravity???? As I confessed, I can follow the math of the simpler case of electromagnetism but cannot follow the more complicated GTR.
I'm afraid I cannot exclude the possibility that I am talking crap, and that this philosophical problem of an "inertial frame" is not related to GR.