help to understand the guage

The gauage in the pattern is described as being "11 sts and 16 rows = 4" (10 cm)".  What does this mean?  Are their 11 sts in 1 inch or in 4 inches?

If the pattern gauge says 11 sts and 16 rows = 4 " (10 cm) it means 11 stitches will give you 4 inches or 10 cm and 16 rows will give you 4 inches or 10 cm.

On a ball of yarn, all guage is based on a four inch square.  It also depends on the correct needle or crochet size.  Your pattern is saying if you use the needle it suggests for that yarn - number is sitting at the top of the little square - you should have 11 stitches across for 4 inches and 16 rows down for 4 inches.  You show make a little sample for yourself of a little more than 4 inches.  So knit 15 stitches for 20 rows.  You should have a square bigger than 4 inches.  Then measure the 11 stitches across and 16 rows down and see if it is in fact 4 inches.  You want to do it slightly bigger because it is easier to see the correct number of stitches and rows.  Everyone knits differently, so you should make a square before starting a project that needs to have the correct gauge.
Hope that helps.

I understand that I should divide the 11 sts in the guage by the 4 in 4 inches to get the approximate number of stitches per inch which is about 3.