Binary addition is much like your normal everyday addition (decimal addition), except that it carries on a value of 2 instead of a value of 10.
For example: in decimal addition, if you add 8 + 2, you get ten, which you would write as 10. While doing this procedure, there is a digit 0 and a carry of 1. Something similar happens in binary addition when you add 1 and 1: the result is two (as always), but since two is written as 10 in binary, we get, after summing 1 + 1 in binary, a digit 0 and a carry of 1.
Therefore in binary:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (which is 0 carry 1)