It's an entry in the blockchain. A record in a database.
Let's say you go to Sotheby's and you buy Van Gogh's Starry Night at auction. Along with the actual painting, you'd get a certificate of authenticity showing the provenance of the work. Basically, a record showing everyone who owned it before you and certifying that this is, in fact, the real Starry Night that Van Gogh painted. The real value of the painting is not in the painting itself, but in that certificate proving that it's the real original. If you tried to sell the painting without it, you wouldn't get many buyers. There's lots of people who could paint an exact replica of Starry Night, but there's still only one real Starry Night. Likewise, anyone can make a copy of a piece of digital art, but there's only one NFT, and if you don't have the NFT in your crypto wallet, you don't actually own it.
So, think of it as a certificate of authenticity for digital artworks, although it can be used to represent ownership of other things as well, if people agreed to it. It can also do neat things like transfer a portion of the sale price back to the original artist every time it's sold, which isn't currently done with regular artworks.