Each IOU is actually a promise to work. Before money it could have been 'I will work for you 30 years' and if someone believes that, they can trade that promise for a nice house for the person to live in. A promise is basically analogous to a debt.

In todays world, the promise is made to a lender (a bank), which then creates a fungible IOU, i.e standard currency for that promise, which can be exchanged for equivalent amount of work.

The whole system is a collective promise to work, and that keeps the society running.