A non-fungible token means a token that is unique. So unlike a dollar note which could be exchanged for any other dollar note of the same amount (fungible), a NFT is uniqu. If I hold it you can't hold it, nor could you replace mine with your NFT.

At the moment there is a lot of hype around representing the ownership of art (digital like a special GIF) or real (like a real painting) as a Token. If you have that token (in your wallet), you own it. If you transfer that token to another person (e.g. when you sell it) he/she owns it now.