The term amplitude refers to the height of a wave, e.g., for a wave described by the sine function, the distance from the function's mean value to its peak value, which is the number multiplied by the sine function. The term is used in descriptions of sound waves, of the waves carried by electrical circuits and can be used for electromagnetic radiation though often other measures are used that carry the same information.
f(t) = m sin t
Amplitude is a commonly-used term within quantum mechanics: it is literally the a amplitude in wave mechanics, one version of quantum mechanics. This wave-amplitude is the square-root of the probability of some phenomenon occurring, and in some cited calculations you see references to amplitude as the square root of the probability even if the association of with waves is not evident. This amplitude is of high interest because the quantum-mechanics calculation of a situation's future probabilities depend not merely on a current probability but on which of its two possible square roots is the associated wave's amplitude.