What is the definition of free fall?
A body is in free fall if it is moving without any external forces acting on it.
First of all it is necessary to put this into context. According to Newton, free fall is motion in the absence of external forces except for gravity.
Einstein showed that gravity is not a force. It is the result of curved spacetime. In terms of relativity free fall is motion along a geodesic which is the four dimensional equivalent of a straight line.
Free fall can be something moving in free space. It can be something falling due to gravity. The most common form of free fall is something in orbit. The Moon is in free fall, as is the ISS. If you are in a ship in free fall you will be weightless.
Most things in free fall are following a geodesic in a gravitational field. So, gravity is responsible for most forms of free fall.