NFT stands for Non-Fungible Token.
The concept of fungibility can only be applied to a group of items. For a group of items to be fungible means that every member of this group is identical to the other, such that no member possesses any individuality.
This means that every member of that group can always be traded for another member without any friction. Some fungible tokens include fiat money, BTC, ETH, and DOT.
BTC is regarded as a fungible token because every BTC is created equal. Further, no BTC is different from another BTC (with certain exceptions we won't get into). The same goes for all the fungible tokens in the crypto-sphere.
Now, if fungibility is the quality of a thing to be interchangeable with other members of its group, then non-fungibility is its ability to have an identity, to be unique. That is all there is to it.
Thus, a non-fungible token is a token that is unique unto itself, so long as only one copy was minted (created) when it was added to the blockchain. So when you hear of NFT collections today, it usually means that they are a group of art pieces composed of unique individuals.
But NFTs are more than just art. It is best to think of NFTs as a sort of new technology. The main point is that they can be used to proof ownership of anything—art, code, films, music, and much more.