What do those numbers at the start of a piece of music mean?

Numbers such as 4/4, 3/4, 2/4, 6/8 and so on which appear at the beginning of a line of sheet music are called "time signatures". The top number tells how many beats are in each measure, while the bottom number tells what kind of note gets one beat (one count).

For example, in 3/4 time there are 3 beats in each measure, and a quarter note gets one count. If the time signature was 3/2, there would still be 3 beats in each measure, but a half note would get one count.

In 6/8 time there are 6 counts per measure and an 8th notes gets one count.

There can be "odd numbers" such as 3, 5, 7, 9 on top, but never on the bottom, because the bottom number describes the kind of note that gets one count, and there are no "3rd notes", "5th notes", and so on -- just half, quarter, eighth notes, etc.