As the others have said, it represents the tempo.  Don't forget to look at the time signature also.  In the first example, 4/4 is the time signature, which means there are 4 beats per measure (represented by the upper 4) and the quarter note gets one beat (represented by the lower 4). Each of the notes in the first measure of the first example are 1/8 notes so for every two of them there is one beat, counted One-and, Two-and, Three-and, Four-and, which equals 4 beats, but you've played 8 notes.