Too Long; Didn't Read
In a similar manner to how a museum keeps records of who owns what artwork, non-fungible tokens (NFTs) allow the blockchain keep a record of the owners of valuable assets.
Because of NFTs, the saying "possession is the not the same as ownership" rings true now more than ever, at least in the case of digital media (images, 3D art, GIFs, and videos).
That's why Justin Bieber paid $1.3M for "an image" you could easily download online. The image (which anyone can possess) holds little-no-value, but the token (which is owned only by Bieber) is worth millions.