“What is the meaning of the words Adagio, Andante, and Allegro?  Are they just indications of speed?  They serve as such; though our musical ancestors probably selected these terms because of their indefiniteness, which leaves a certain margin to our individuality. Literally Adagio (ad agio) means “at leisure.”  Andante means “going” in contradistinction to ‘running,” going apace, also walking.  Allegro (a contraction of al leg-gie-ro) means with “lightness, cheerful.”  Primarily these terms are, as you see, indications of mood; but they have come to be regarded as speed annotations.”

…Josef Hofmann, from his book, ‘Piano Playing’.