For a physical quantity that changes periodically, the amplitude is a measure of how much the quantity changes from maximum to minimum. The simplest example is a sine oscillation. Over time, the sine curve oscillates between its minimum and its maximum values and the amplitude measures how big this oscillation is. There are different ways of defining amplitude. Some definitions use the Peak-to-peak difference for the amplitude (Maximum of the signal minus Minimum of the signal). Other definitions for signals with values centered symmetrically around zero specify the amplitude as the maximum value of the signal (Half of the Peak-to-peak amplitude).
Depending on the nature of the oscillation or wave, the amplitude will have different meanings. For a pendulum swinging back and forth, the amplitude is the maximum angle between the vertical direction and the pendulum string. For an electromagnetic wave, the amplitude is the maximal value of the electric field or equivalently (since the two maxima are related) the maximum of the magnetic field. For a (weak) gravitational wave, the amplitude is a direct measure of the changes in distance caused by the wave – as a simple gravitational wave of amplitude A passes, there are two directions in which distances are alternately stretched by up to a factor (1+A/2) and compressed by a factor (1-A/2).
The amplitude can change over time. For instance, for an ordinary pendulum, air friction will slow the pendulum bob down, and for each period – for each time the pendulum bob travels back and forth – the amplitude will be less than for the previous period. For a wave, the amplitude will also in general vary with location. Typically, the amplitude of a wave will decrease with the distance from the wave’s source.