Can someone explain to me how your parents can be cousins to each other? I've never really understood how that works and it would be great if someone could tell me exactly how that happens.

I don't know because 20 years ago it was illegal. Its only recently that some states have made it legal.
Your mother and father would have to have married their mother or fathers brother or sisters kids to be cousins.

How can your parents be cousins?

Well, if their parents are related, brother and sister, sister and sister or brother and brother, then they're cousins.

Sorry, had to do it.

It's no longer illegal, it's just frowned upon.