Acceleration is the rate of change of velocity over time. As a simplification, it is the rate at which something speeds up or slows down.
Acceleration describes the rate of change of both the magnitude and the direction of velocity (vector).
In relativity theory, proper acceleration is the physical acceleration experienced by an object. It is acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. This contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers. [Wikipedia]