It adjusts its format according to the brackets,paranthesis, etc according to the size of the expression contained within it.

For example:

Without \left and \right

If you type [\frac{\frac12}{\frac12}] = 1 you get $\displaystyle [\frac{\frac12}{\frac12}] = 1$

The square brackets are small compared to the expression inside and they look ugly

However with \right and \left

If you type \left[\frac{\frac12}{\frac12}\right] = 1 you get $\displaystyle \left[\frac{\frac12}{\frac12}\right] = 1$

The square brackets are now properly reformatted and looks nice.