unable to understand cosets

The definition of coset is as follows

http://i291.photobucket.com/albums/l...apture8475.jpg

However, I am still not able to understand what this means. An example shown is

http://i291.photobucket.com/albums/l...apture4395.jpg

I do not understand how 3 + H = {3, 1}. 3 does not belong in H. and I also don't understand 2+H = {2, 0}.

I can't make out much from the textbook. Where can I learn this material? I would like to see some more simplified and friendly defintion. In fact for past couple of hours I am struggling to get a grasp on cosets.