In the theory of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.

Quotes

• We postulate: It shall be impossible, by any experiment whatsoever performed inside such a box, to detect a difference between an acceleration relative to the nebulae and gravity. That is, an accelerating box in some gravitational field is indistinguishable from a stationary box in some different gravitational field. How much like Einstein this sounds, how reminiscent of his postulate of special relativity! We know the principle of equivalence works for springs, (as we knew special relativity worked for electrodynamics), and we extend it by fiat to all experiments whatsoever. We are used to such procedures by now, but how originally brilliant it was in 1911—what a brilliant, marvelous man Einstein was!
  • Richard Feynman, 1962-63, in Feynman Lectures on Gravitation (1995), Lecture 7

• In fact, how could you tell inside a space ship whether you are sitting on the earth or are accelerating in free space? According to Einstein’s equivalence principle there is no way to tell if you only make measurements of what happens to things inside!
  • Richard Feynman, in The Feynman Lectures on Physics, Vol. II (1964), 42-5 Gravity and the principle of equivalence

• [T]he gravitational force allows us to declare that all observers—regardless of their state of motion—are on absolutely equal footing. Even those whom we would normally think of as accelerating may claim to be at rest, since they can attribute the force they feel to their being emersed in a gravitational field. In this sense gravity enforces the symmetry: it ensures the equal validity of all possible observational points of view, all possible frames of reference.
  • Brian Greene, The Elegant Universe (1999/2003) Ch. 5 The Need for a New Theory: General Relativity vs. Quantum Mechanics.

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