The term Relativity is used for two theories developed by Albert Einstein that accommodate the apparent constancy of the speed of light, even to someone traveling fast in the same direction as the light beam. The constancy was evident in the Michelson-Morley Experiment, which strove to find the velocity of Earth as compared to Ether, the name given to whatever substance has the waves that we perceive as Electromagnetic Radiation. The Lorentz Transform (or Lorentz Transformation) was a mathematical attempt to explain the apparent constancy through effects of motion on the dimensions of objects. Einstein used the transform to develop a consistent model of nature that matched experiment at the cost of throwing away our preconceived notion of simultaneity: that whether two events are simultaneous depends on the relative motion of observers. The theory demands the Lorentz Transform rather than the Galilean Transform (or Galilean Transformation), which matches our intuitive senses and everyday experiences, but at typical everyday speeds (aka Non-Relativistic Speeds), the two converge.
Relativity shows how even though you and your surroundings may be in motion, that motion isn't evident unless you can observe something moving relative to you. In addition to Einstein's conceptions the term is also used for earlier explications of this concept, that didn't take into account factors evident more recently when Einstein tackled the problem.
Einstein-de Sitter Model
General Relativity (GR)
Gravitational Wave (GW)
Radiation Hydrodynamics (RHD)