Time signatures help count the rhythm of written music.
They come in a whole range, here's a brief guide to the common ones:
Simple time:
2/4 - count 2 per bar (1 and 2 and)
3/4 - count 3 per bar (1 and 2 and 3 and)
4/4 - count 4 per bar (1 and 2 and 3 and 4 and)
Compound time:
6/8 - count 2 per bar (1 and a 2 and a)
9/8 - count 3 per bar (1 and a 2 and a 3 and a)
12/8 - count 4 per bar (1 and a 2 and a 3 and a 4 and a)
A few others:
common time - count 4 per bar, as 4/4
alla breve - count 2 minims per bar
cut time - count 2 per bar, as 2/2
And more:
5/4 time - count 5 per bar
7/8 time - count 7 per bar
etc
Also see Key Signatures.
Read more: Wikipedia