There are basically two theories of their value: the collectible theory and the ownership theory. These overlap but are best explained separately.
In the collectible theory, NFTs are like an autograph you get on merch from a famous person. Think an autographed photo of Will Shatner you might get at a con. Usually the (cryptographic) autographer is the original artist of the work being autographed. Of course the autographer can release multiple autographed versions of the same work, but this decreases their value (and the value of any further work they might autograph).
Collectibles have long had value to humans, but they also suffer from three annoying problems: storage, fakes, and transaction costs. NFTs solve all three - they never degrade on the blockchain, their authenticity is cryptographically verifiable (assuming one can associate the signing address with the famous person, which is comparatively simple), and they are easily transferred online.
The second theory is the ownership theory. Here NFTs are used to track ownership of the underlying digital asset. In our current internet this is absurd, as the torrent is designed to demonstrate - everything is a copy, and even the NFT holder can never get access to the "original" bits. The ownership theory requires adoption of NFTs as an ownership mechanism in the metaverse, along with associated digital rights management technology. It's an early land-grab for the VR overworld.
Now, personally I don't find either of these theories very compelling. But I also didn't find cryptocurrencies generally very compelling, so I don't have a great track record. Cryptocurrency really tends to turn us all into Frank Grimes -like characters who miss out. I believe the more widely-used term is "midwit".