The Special Theory of Relativity allows us to compare observations and measurements made by observers in two reference frames that move at constant velocity relative to one another (inertial frames). All the genuine laws of physics take the same form in both frames eg
and 
Einstein felt that the Laws of Physics should take the same form in all reference frames, including frames that accelerate relative to one another. He extended the Theory of Special Relativity to cover this using The Principle of Equivalence – the idea that observations made on an object cannot distinguish between a force of nature and an accelerated reference frame. Suppose for example that a spaceship floating in space stated it's engines, causing an acceleration of
Passengers floating freely inside the spaceship would appear to any passenger strapped in, to fall to the floor with acceleration g, even though in fact, the ship is accelerating to meet the stationary passenger. When the passenger reached the floor, they would be able to stand, throw and catch a ball, play tennis etc just as on Earth.
Einstein reasoning led him to the conclusion that objects travel in a curved four dimensional spacetime: spacetime itself is distorted by the presence of matter and energy. Spacetime is curved, so that a straight line between two points becomes in spacetime, the shortest distance which may not be a straight line in space.
For the sphere shown above, the path followed by a particle from A to B is the arc AB, not the straight line between A. Space here may be thought of as the surface of the sphere, along which the particle must travel.