Fungibility is a property of money and commodities. It means that each unit can be exchanged for each other unit. Fungibility is very important for Bitcoin if it is to be a good form of money. Every satoshi should be equivalent to every other satoshi.
If one can meaningfully distinguish one coin from another, then the fungibility of the money is weak. If fungibility is too weak in practice, then bitcoin cannot be decentralized: if someone important announces a list of stolen coins they won't accept coins derived from, you must carefully check coins you accept against that list and return the ones that fail. Everyone gets stuck checking blacklists issued by various authorities because in that world we'd all not like to get stuck with bad coins. This adds friction and transactional costs and makes Bitcoin less valuable as a money.
Better Privacy in bitcoin can help with long term fungibility of bitcoin.