Yes, the tempo describes the speed of a composition; it literally means "time" in Italian.
"BPM" stands for beats per minute; it's the musical equivalent of "miles per hour," and it is the standard way of measuring the tempo of a composition.
But the tempo is different from how many notes are played. A piece with a very fast tempo could use relatively few notes, whereas a very slow piece could use many many notes.
To go back to the "miles per hour" analogy, imagine driving 60 miles an hour but only passing two trees. Now imagine driving 1 mile an hour and passing 100 trees. Which is the best measurement of speed, miles per hour or trees per hour?
This is why it's more common to measure the BPM of a piece instead of the number of notes per minute.