The mean (also called the average) is a measure of where the center of your distribution lies. It is simply the sum of all observations divided by the number of observations.

The mean is strongly influenced by extreme values.

For the precipitation data, the mean is:

(2 + 3 + 10 + 5 + 4 + 4 + 3 + 3 + 1 + 2 + 3) / 11 = 3.636.

Even though most months (7 out of 11) had 3 days or less of precipitation, the mean is close to 4. The extreme value of 10 days with precipitation for April is affecting the mean quite a bit. Without this observation, the mean would be exactly 3. On the other hand, if you include an April with 30 days of rain instead of 10 in the calculations, the mean would be 5.455, a value that is greater than all but one observation!