Various people/organizations buy these bonds and give the US government money. Later on these bonds "mature" and those people get their money back plus some interest.
This post is saying that about 9 trillion dollars worth of these bonds will mature in the next 4 years so the US government will need to come up with that much money to pay the bondholders. The way the government does this (for the most part) is by "rolling over" the debt. This means the government will issue new bonds that pay out at some point in the future.
In some ways this is actually great for the government because interest rates are at very low levels right now, which means the new bonds will (in most cases) have a lower interest rate than the old ones.
Just what I came here to mention. The debt that matures will almost certainly have had a higher interest rate than whatever the amalgamated rollover rate will be.
https://www.gurufocus.com/yield_curve.php
Historically this means a recession is coming. The reason is that investors are thinking that other investment options are not good, so they are parking their money in safe bonds.
Anyway, this is good for government dept I guess.
Government dept is held mostly in short term, so the percentage of government spending used to service dept is very quickly tied to interest rates. Things can go bad fast if interest rates go up.
Ignoring a great deal, basically that debt either needs to be paid off when it matures or rolled over into bonds e.g. issuing debt to receive cash that can be used in paying off those bonds.
Now, how that will affect the USD is where things get complicated. Will a higher interest rate be needed on new financing to attract investors? Will the Treasury have cash on hand to cover paying off all of those?
Assume they goto the market to refinance all of those bonds and have to pay a higher interest rate: this means tax payers have to pay more taxes, and get less services because more of their money is going to interest payments on this debt. Or perhaps they can only find investors willing to buy 8 trillion in new bonds, then that means the budget needs to cut out 1 trillion for that year in services, just to give a couple ways how this could play out.
Everyone has their own idea of what will happen and will speculate accordingly. Some might think interest rates will explode, of the Fed might cut. Maybe Foreign flows will not be reinvested and affect the USD accordingly. Etc, etc, etc...
In that sense, they set the "risk-free rate of return" by which other investments are baselined. Not happy with the 2.5% (or whatever) on a Treasury? Well, you might want to invest in a state/municipal bond, or a company's bond offering, mortgage-backed-securities, or stocks. You would only invest in those riskier investments if they promised to pay you a rate higher than the "risk-free" rate of Treasuries.
In that regard, rising Treasury rates increase the market-clearing interest rates on any borrowing which is considered riskier than the US government's likelihood of non-payment, so in short, on all other sorts of borrowing. (On fringes, this may not be the case where statutory limits apply, such as on credit-card default rates. If the risk-free rate rises high enough though, such lending might be curtailed in favor of simply moving down the risk ladder if the returns become artificially compressed.)