Tempo describes how many pulses occur in a given unit of time and is normally measured in units of beats per minute (BPM). The notion is very simple, but here are four points regarding tempo that you may find interesting or useful:
Point #1. Your heart typically beats about 60-80 times per minute (about once every second). And it just so happens that most musical tempos range from about half that on the slow side to twice that on the fast side. Is this just a coincidence or is there some organic relationship between our perception of tempo and the human pulse rate? Perhaps some other aspect of human perception is relevant?
Point #2. Tempo can have an enormous effect on the emotional impact of a piece. Some lively pieces are begging to be played fast and some reflective pieces are aching to be played slowly. And some pieces are particularly “sensitive” tempo-wise: Going just a few percent faster can make the music feel rushed and just a few percent slower can make the music feel like it’s dragging.
Point #3. Some classical pieces come with very specific tempo indications, as seen below.
View such markings as a ballpark suggestion, not a rigid rule. Trust your artistic judgement of what sounds and feels musical.
Point #4. Tempos are not typically intended to be followed with machine-like precision from the first to last note. Subtle tempo variations are an essential part of any natural-sounding performance. Artistic phrasing invites a tasteful acceleration here and deceleration there… or for one hand to play the accompaniment “in time” while the other hand takes expressive liberty with the melody (known as rubato).