What does it mean when your credit report says you have 3 open accounts?

It doesn't necessarily mean that you owe money. A credit card or line of credit that has a zero balance but has not explicitly been closed would still be considered "open". It means you could still borrow from it if you needed to. It's also possible that the account is actually closed but the creditor has not yet informed the reporting bureau(s) of that.

A closed account is one that has been reported as "closed", meaning no more activity is allowed on that account. Most term loan accounts (like a mortgage or car loan) are reported as closed as soon as they're paid in full. Revolving credit lines are kept open until explicitly closed by the borrower.