If you look at the truth table for the OR gate not only does the output go high when A OR B are high but it goes high when A AND B together are high. 
This can cause problems in some applications.

Therefore the EXCLUSIVE OR or EXOR is used.

The output of the EXOR only goes high when A or B on its own goes high.
That is when A or B exclusively goes high.

When A and B are both high the output stays low.

This is shown in the truth table.