Fungibility is a property of goods which are interchangeable and indistinguishable. For example, pennies are all worth $0.01 and ownership of one penny is not preferable over any other penny.
Fungibility is a desirable property for Bitcoin in order to maximize Bitcoin’s utility for individuals. If certain bitcoin are considered tainted, perhaps because of past ownership by criminals, those bitcoin could be deemed less valuable by regulated merchants or exchanges. Merchants could be required to check each bitcoin received to ensure they were not tainted. These restrictions would place immense burdens on consumers, merchants, and exchanges, discouraging adoption of Bitcoin.
Privacy mechanisms such as CoinJoins attempt to ensure that bitcoin remains fungible in the future by providing a secure way of obscuring the past ownership of certain bitcoin, rendering the concept of taint unusable.