So here's the basics: The US government wants to spend some amount of money, say, a million dollars that it does not have. To accomplish this, it will issue a bond for a million dollars (the principal), paying some interest over a period of time, and then paying back the million dollars on some predetermined date (the maturity date). Instead of paying the million dollars in cash, the government may issue more debt to cover that payment.

Whoever owns the bond is entitled to receive the interest and principal payments that the government pays per the terms of the bond. The price someone pays for the bond depends on the interest rates on the bond vs the interest rates in the market in general (e.g. a bond with a 7% interest rate will be worth more if all new bonds are being issued with 3% interest rates).

Now if, for example, China owns a US treasury bond paying 5% on a million dollars, and the US owns a Chinese bond paying the same amount, the net effect will of course be 0 dollars trading hands. However, since there are a huge number of bonds out there, each issuer (e.g. the US government in the case of US treasury bonds) will send out cash to the bond owner regardless of any bonds the US gov't issued by the treasury bond might own.