Systematic experiments on freely falling objects were carried out by Galileo Galilei (1564-1642).

Freely falling objects are objects not supported by anything and not acted on by any forces except the gravitational force.  Near the surface of the earth such objects are accelerating.  This acceleration is due to the gravitational force acting between the objects and the earth.  The direction of the gravitational acceleration vector is towards the center of the earth.  Its magnitude decreases as one over the square of the distance from the center of the earth.

The radius of the earth is 6368 km.  If you climb a 1000 m high mountain, your distance from the center of the earth changes by (1/6368)*100 % = 0.016 % and the magnitude of the acceleration vector changes by (1/6368)2*100 % = 2.4*10-6 %.  For all objects near the surface of the earth the distance from the center is nearly constant, and the magnitude of the gravitational acceleration vector is therefore approximately constant.  We denote the gravitational acceleration vector by g.  Its magnitude is g = 9.8 m/s2 and its direction is straight downward.  Over small distances, when the curvature of the earth's surface can be neglected, the direction of the gravitational acceleration vector is also nearly constant.

Near the surface of the earth g is the same for all objects.  All objects accelerate at approximately the same rate.  Freely falling objects are therefore objects, which are moving with constant acceleration g.