A debt is a very natural thing for humans, because we feel compelled to provide value to people who can't pay us yet.
Even before money people had gifts and favors - we give with the expectation that we'll be given something in the future - or we say 'you owe me one' when someone has helped us through an issue without sending us an invoice.
So the genius of fiat currency is that you get to represent these IOUs as a standard, fungible currency, such that I can take the debt you owe me and transfer it to someone else, so now you owe them. Being able to trade debt like this essentially turns debt into the currency.
The benefit of this being that economic growth is not limited to how many gold coins we can mint -- we can become as indebted to each other as we like -- the more people go into debt, the more money we have to trade. Pretty neat.