I mean, why does anything have value?

In the strict financial sense, something is only worth what somone else is willing to pay for it. That's the whole premise of financial trading. Getting a bit beyond ELI5 now, but most exchanges use something called a Central Limit Order Book (CLOB) to let the participants in the market see who wants to buy and sell what and for how much, and also to match those buyers and sellers. This is a good intro: https://optiver.com/explainers/orders-and-the-order-book/

In terms of shares in companies, then they do have some fundamental value according to the market. If you buy a share in the company, you get a share of the profits (paid as dividends), which gives those shares some value. Obviously, there's a lot of speculation too as people are involved, so emotions and wild predictions can come into play!

Financial instruments that get traded aren't limited to shares in companies though. There are all kind of other financial instruments that get traded every day, some are pretty basic like buying and selling different currencies. Others involve all kinds of crazy financial engineering , like the sort that caused the crash in 2008!

Most have some fundamental value based on their attributes, so it's a little different to the likes of an NFT. The big issues come if the values that the market has agreed upon don't match reality, which is what happened in 2008.