Albert Einstein's Theory of Relativity is a set of two theories in physics, special relativity and general relativity. The core idea of both theories is that two observers who move relative to each other will often measure different time and space intervals for the same events, but the content of physical law will be the same for both.
Special relativity, developed in 1905, only considers observers in inertial reference frames which are in uniform motion with respect to each other. The theory postulates that the speed of light in vacuum will be the same for these observers. This leads to redefinitions of such fundamental notions as time, distance, mass, energy and momentum with wide ranging consequences. Moving objects become heavier and shorter; moving clocks go slower. Light has momentum. Two events may be judged to be simultaneous by one observer but not simultaneous by another. The speed of light emerges as an upper limit for the speed of matter and information. Mass and energy are seen as equivalent. The theory does not account for gravitational effects.
General relativity was published by Einstein in 1915. It uses the mathematics of differential geometry and tensors in order to describe gravity. The laws of general relativity are the same for all observers, even if they are accelerated with respect to each other. General relativity is a geometrical theory which postulates that the presence of mass and energy "curves" space, and this curvature affects the path of free particles (and even the path of light), an effect we interpret as a gravitational force. The theory can be used to build models of the evolution of the universe and is hence a crucial tool in cosmology.