Keeping it very simple:

The government sells tickets for which buyers pay $100. If the 10-year treasury bond rate is 10%, tickets can be turned in after ten years to get $110. If the government uses the $100 they get at the start to build something which allows them to collect at least $110 in taxes, (things like infrastructure to enable commerce, or educational spending to increase personal income, etc.) it covers its costs. There are complexities but this is the boiled down version of how many government activities are funded through debt.

As for who is owed the debt, it’s whoever holds the tickets. They can be bought and sold at will so investors trade them regularly. They are generally the low-risk/low-reward option for investment because they don’t usually pay a great rate, but will only be a loss if the country itself collapses.