It's really strange. I do appreciate that you are basically buying a certificate of authenticity that represents ownership of an idea, and that it is trackable on a blockchain. It sounds bizarre conceptually, but then if you think to crypto in general - and also how credit cards and bank accounts represent actual money, well it begins to sound less strange. Like everything else, it is just what people have agreed has a value, at that point it simply does. It was made pretty clear to me, when someone mentioned that it's similar to how people will buy fine art and then keep it in storage. They own it, it has worth, but the idea of it is bigger than the fact that it might actually exist somewhere or even actually be on display.
One of the really interesting wrinkles of it, is that the original creator of an NFT will get 10% of each sale of an item in perpetuity. That famous Beeple piece that started the current media fascination was originally sold for $66k, and this past March was resold for $6.6M - netting him $660,000. Not bad!