NFT is short for Non-Fungible Token. Simply put, non-fungible means that each NFT is unique, and one token isn't necessarily a good substitute for another token. This differentiates from ordinary cryptocurrencies and utility focused tokens such as Bitcoin or Ethereum, which are fungible tokens.
In the case of currencies and cryptocurrencies, it is very important that different units of the same currency are the same (fungible). Without this then they are unable to be used as an effective medium of exchange. Perhaps the best example of this is the US dollar (or your equivalent fiat currency). If we both had separate dollar bills and swapped them, there would be no change in either of our financial positions. Because dollars are homogenous (or fungible) and everyone knows exactly what they represent, they become a very effective medium of exchange and short-term store of value. This is what makes them the most important transactional currency in the world.
Contrast this with NFTs however and the situation is very different. If we both had 1 NFT and swapped them this could result in a very marked change in our relative financial positions. The reason being that my NFT may be incredibly rare and desirable while yours could be a very common and undesirable. This difference in features and desirability can result in each NFT having vastly different worth. This is the same with many real-world items too, which is why you wouldn't swap a Ferrari for a fiat punto. Both are cars, both drive you from a to b, but they are not suitable substitutes.
In this sense it is perhaps easiest to think of NFT's as digital collectibles. However, while this is currently their main use case, they also have several more productive applications. Perhaps the biggest of these being their ability to monetise and protect intellectual property that is currently very vulnerable to theft and piracy. This is particularly prevalent in the music, tv, sports and entertainment industries where piracy and illegal streaming is rife. By using NFT's as unique online 'keys' that must be purchased before you can view or access content it can help to solve this problem and ensure that artists and creators are better remunerated for their content. Furthermore, on a blockchain based database the sharing of NFT protected content to anyone without the required access would be impossible as the ledger wouldn't permit the transaction to take place.
Overall NFT's are completely different to 'ordinary' tokens which most people are familiar with. While their uses can be novel, they also make up an important part of blockchain infrastructure and their use will only continue increase as blockchain technology becomes more prevalent.