Count a beat to four. 1-2-3-4 and start stomping the beat. Now count to eight over that beat. For every 1 beat you stomp, count two beats. (1)1-2-(2)3-4-(3)5-6-(4)7-8. 1 should be on the 1, 3 on the 2, 5 on the 3 and 7 on the 4. Now you're counting 8th notes over a 4th note beat. Now try counting 4 times per 1 beat. Knowing mathematics, you know it brings you up 16 counts per measure.
Take a visual example as well.
| represents a 4th.
! represents an 8th.
. represents a 16th.
|.!.|.!.|.!.|.!.
As you can see the 4-beat measure here is divided into 16 digits.
A 16th note says something about how long a note is played. If for example you play in a tempo where you have 80 beats per minute(4th notes), you can play quadruple that in 16th notes, bringing you up to 320 16th notes per minute. It's all math really. Playing 16th notes is just another word for playing really fast.
I hope that wasn't too confusing for you.