The equivalence principle is the idea that gravity is just a fictitious force, equivalent to other fictitious forces such as centrifugal force or the Coriolis force. That is, the force felt by someone standing in the Earth's gravitational field is the same as the pseudo-force felt by someone in, say, an elevator in outer space being pulled by a rope attached to a spaceship accelerating at 9.8 ms-2.
This principle was first enunciated by Albert Einstein as the starting point for the general theory of relativity. He formulated gravity as a special kind of fictitious force, arising from the curvature of spacetime. But the idea of fictitious forces was known in classical Newtonian mechanics, and the very similar nature of gravity had been noticed before, for example, by Johann Soldner in 1803.