Charity Sunday is the Sunday after Thanksgiving. Which means that it is also the Sunday after Black Friday, one the the biggest spending days of the year, if you live in the USA. It is also called 'White Sunday', but at this point if you refered to 'White Sunday' without context most Americans wouldn't know what it meant. As a matter of fact, most of them might be confused by the phrase Charity Sunday as well.
While Small Business Saturday and Cyber Monday are pretty well established (and hyped), Charity Sunday is not. It is theoretically a day to make a charatible donation to a worthy cause, although in fitting with the shopping theme some sources focus on the opportunities to shop from stores that support good causes, while others focus on making charatible donations in place of gifts... or even, perhaps, entirely on their own merit.
Currently Charity Sunday is entirely a fringe movement, and I'm not certain that that's bad. Charity should happen much more often than once a year, and it is unlikely that most people will be the most charitable just after they dropped a lot of money on one of the biggest spending days of the year... and are expecting to spend a lot more tomorrow. However, if it does encourage people to keep charitable giving in mind, it is not a bad thing.
If you are looking for a site to give, or to give-as-a-gift, I recommended Watsi, although there are many other options out there.