what does it mean the earth is curving away during freefall?

Question

is it because the earth is rotating?
or, because the earth is just falling in space?

Answer 1

A free falling object is "geo stationary". As the earth is moving, the object that falls at the same point whence kicked describes a curve not a straight line.

Answer 2

Correct, the Earth is falling due to the gravity between it and the Sun. It's momentum due to orbit, however, just compensates enough for this curving or falling to keep us in orbit.