Beats per minute (or BPM) is a term used to describe the number of beats per minute in a piece of music.
In every piece of music there are a number of beats per bar. The length of each beat depends on the time signature. For example, 4/4 means that there are 4 beats per bar (top number 4) and that the note value is a crotchet note, or quarter note (bottom number 4). 4/4 time signatures are often marked with a C.
The tempo is then used to suggest the speed of the music. So, if a piece has an adagio tempo, it should be played slowly. To get an idea of what that speed is, we can use BPM: For adagio, it is generally between 66 to 76 BPM.
To sum up: two pieces of music which both have the same time signature (for example, 4/4) will not necessarily be played at the same speed. Even two pieces which have the same tempo marking (for example, andante) may be played at different speeds because they have a different number of BPM.