It means "must/have to". For example: "I can't afford not to finish the project today." It means I must finish the project today, otherwise something might happen. Another sentence: I can't afford not to wake up early tomorrow. It means I have to wake up early tomorrow, otherwise I might be late going to work. CMIIW. Hope it helps.

Think about it like this: You can't afford to pay the consequence of not doing the thing you say you "can't afford to do". Essentially that's what you are saying - that you can't afford the cost of not doing something. So, yes, basically you need to do it - not in the sense of being required to by someone else, but in order to avoid some more negative consequence.