General Relativity uses the ideas of time dilation and length contraction to explain gravity.
The thought experiment goes that if you are inside an enclosed lift with no windows in outer space, you would not be able to tell if you were falling in a gravitational field. You (inside the lift) would be falling too and so you would feel just as weightless as in outer space. This expresses an *equivalence* between motion and gravity, although I am simplifying quite a bit.
If you were falling however, you would be accelerating towards some planet and therefore you would observe the effects of time dilation and length contraction. All the clocks on the planet would appear to tick slower than yours and all rulers pointing radially out from the planet would be shorter than your upright ruler in the lift. The terminology for this is to say that space-time is warped by a gravitational field. The common image used is one of a ball bearing on a rubber sheet; it bends the sheet much like gravity from the planet bends space-time.
Since you started your free-fall a long way out, your ruler and clock would agree with any ruler and clock in the flat region of space a long way from the planet. It is *your* ruler and *your* clock inside the lift that are the reliable 'flat space' measures. All the clocks and rulers on the planet are "wrong" according to you, space-time has been 'warped' near the planet.