The basic postulate of A. Einstein's general theory of relativity,
which posits that an acceleration is fundamentally
indistinguishable from a gravitational field. In other words, if
you are in an elevator which is utterly sealed and protected from
the outside, so that you cannot "peek outside," then if you feel a
force (weight), it is fundamentally impossible for you to say
whether the elevator is present in a gravitational field, or
whether the elevator has rockets attached to it and is
accelerating "upward."
Although that in practical situations -- say, sitting in a
closed room -- it would be possible to determine whether the
acceleration felt was due to uniform thrust or due to gravitation
(say, by measuring the gradient of the field; if nonzero, it would
indicate a gravitational field rather than thrust); however, such
differences could be made arbitrarily small. The idea behind the
equivalence principle is that it acts around the vicinity of a
point, rather than over macroscopic distances. It would be
impossible to say whether or not a given (arbitrary) acceleration
field was caused by thrust or gravitation by the use of physics
alone.
The equivalence principle predicts interesting general
relativistic effects because not only are the two
indistinguishable to human observers, but also to the Universe as
well -- any effect that takes place when an observer is
accelerating should also take place in a gravitational field, and
vice versa.
See weak equivalence principle.