One of the postulates at the basis of general relativity: A freely-falling observer in a gravitational field does not feel gravity. More precisely: In a small region of space around an observer in free fall in a gravitational field, the laws of physics are approximately the same as without gravitation (i.e. in special relativity) – at least for a time-limited observation period.
This is sometimes called Einstein’s equivalence principle, which includes a more restricted version called the weak equivalence principle, namely that, in a gravitational field, objects which are at the same location are subject to the same gravitationalacceleration – they fall at the same rate (“universality of free fall”).
More information about the equivalence principle can be found in the spotlight topic The elevator, the rocket, and gravity: the equivalence principle, while the path from there to Einstein’s geometric gravity is traced in Gravity: From weightlessness to curvature.