The national debt is largely in the form of Treasury Securities (bonds that are issued by the Treasury Deptment and sold for cash. This cash is used to finance the operations of the US Gov’t). See here for a breakdown of who holds these securities.
So, yes, the government can just create money out of thin air, but the difference between this process and literally printing cash is that here the government has promised to buy back the bonds that are being issued. (That’s how a bond works.) When governments just print cash, that can lead to lots of problems, but this process of bond issuance has proved relatively safe (so far) since everyone believes that the gov’t will indeed pay back the money it’s borrowed.
If we were to pay off the debt, that would be great. We’d do so by collecting more taxes (or selling gov’t owned assets) than are necessary to operate the government and use the extra to pay back this debt.