does it relate to the tempo?
yes. the tempo is measured in 'beats per minute'. so indeed if you increase he tempo, it means the quarter notes will go faster, the whole bar will go faster. the whole song will go faster. tempo markings often show a little note to actually indicate what one 'beat' note is. ♩=100 means there are 100 quarter notes per minute. ♪=100 means there are 100 eighth notes per minute