Pretty much just what you said: how much the data "varies" or is spread out. Essentially, it tells us how "random" the data is.
It is a measure of spread
for more details look here..:
Variance - Wikipedia, the free encyclopedia
The average of several numbers which have been squared is not equal to the average of the numbers then squared.
Suppose you have 2 numbers a and b
The average of their squares is
The square of their average is
You can see that they are different values.