What is the inertial frame?

Question

In the twin paradox, why is the person on earth an inertial system and the person on the spaceship a non-inertial frame?

Answer 1

In the classic version of the paradox it is because the person in the spaceship has to turn around to come back, which means they have to accelerate, which means they are not moving inertially during the acceleration.

There is a way to set-up the paradox that doesn't involve acceleration, in which the outbound twin synchronises a clock with somebody else who is travelling Earthbound, but the resolution of the paradox is the same in both cases, namely that two inertial frames are involved in the outbound and return journeys, and they have different planes of simultaneity, and it is that which results in the overall time difference. If you want a better explanation of that, see the hundreds of questions that have been asked about the twin paradox.