When you're saying something that you don't usually tell anyone, or say in public because you might be embarrassed about it, shy or simply just don't want to tell. Mostly used in a non-serious way, although there may be exceptions: I love her more than I care to admit. (basically would mean: I love her more than I really want to tell anyone/her) I cry whenever I see a sad movie, more than I care to admit. (basically would mean:I cry whenever I see a sad movie more than I want to tell anyone/Let anyone know) He eats more than he cares to admit (basically would mean: He eats more than he wants to tell anyone)

Usually, if they are telling you something which they don't really want to admit to. It would be something fairly light-hearted. I eat more chocolate than I care to admit. I know that I should walk more, but I use the car more often than I care to admit.