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Fungibility is the ability of a good or asset to be interchanged for another good or asset of like kind and same value. Basically it doesn't matter which one you have, only how many.
Hence, goods and assets that are not interchangeable, such as owned cars and houses, are non-fungible.
Fungibility is an important characteristic for currencies to maintain their purpose, reliability and to be exchangeable widely to process daily transactions. Each unit of currency remains the same despite the amount of spending.
In case of crypto, fungibility serves same function as with other fungible assets, including the fluctuating prices. Fungible cryptocurrencies are for example Bitcoin or Ethereum.
Non-Fungible Tokens (NFT) are digital assets (digital representation of real world assets, or unique digital assets) of exclusive nature and properties. Each differs from one another, therefore do not possess the same value and are not interchangeable. NFT possess inimitable metadata that leads way for its exclusive admission on the Blockchain. Non-fungible cryptocurrencies are for example unique creations in the Blockchain game CryptoKitties, where each 'kit' has unique features and exists only one-of-a-kind, with unique digital metadata/ signature.
Non-Fungible Token possess a certain value, like antiquities, art, vintage collectibles, that increases with rarity and/or popularity.
Features of NFT
Unique ownership
Not substitutable by another fungible or non-fungible token
A unique set of characteristics, features - digital data
NFTs are not separable
More details and real-world application of non-fungibility eg. for Intellectual Properties or Incorruptible Record Keeping you can find in my previous short writeup here.
Source: HashCash, Investopia, IWS FinTech