Liabilities
A liability is a debt: either money you owe or money that is owed to you. In Firefly III you can track both of these.
To learn more about liabilities, check out these pages:
You owe money
The general idea of a liability where you owe money (let's call it a debt) is that there is a account with a negative amount in Firefly III that represents the debt. Once you fill this particular hole, the money is yours again.
There is a difference here whether the money is usable by you or not. For example, if you borrowed money, and it was spent on a house (aka a mortgage), the money is "nowhere", and not part of your finances. In other cases, you can transfer money from the debt to your asset account and then spend it.
In both cases the account balance is negative. Sending money to the liability is a "withdrawal", because it withdraws money from your accounts. If you get money from the loan to spend, it's a deposit.
You're owed money
This works almost exactly the same. There's a few differences though. A friend has borrowed 500, and is slowly paying you back.
The liability starts at 500. Every time your friend pays you back, you transfer money from the liability to your checking account. You'll notice that this is a "deposit", and that the "amount due" goes down. Likewise, if you borrow them (more) money, the amount due goes up.