More of a physical representation of a debt, but in essence, yes.

I buy a rock from you with $5, that $5 represents the debt I incurred by taking the rock. You have the $5 that you can use to barter for something else. At the end of the day, the government is backing my debt for the rock with a physical piece of paper. Except it isn't physical anymore now that everything is digital. So, I suppose its more like the bits of data that represent the physical money that represents the debt for the rock is backed by the government. Although that money is actually physical at the bank that conducted the electronic transaction, and they borrowed that physical money from the fed. But even then, it is inflated since not every dollar a bank transacts with, is backed by something physical since the reserve ratio is not 100%. And that is when it starts becoming confusing.

It's also an asset. Trade it for goods and services.