Whenever a user wants to withdraw tokens from the Matic side chain to the Ethereum main chain, the user has to burn his tokens on Matic and then submit a proof of the burn on Ethereum. Once this proof is verified, the user is given an exit NFT as a representation of his proof getting accepted. But the user still has to wait for a period of 7 days in order to actually withdraw his tokens. Once this 7 day period is over the user can again trigger an exit transaction that will burn the exit NFT token and transfers the corresponding withdrawn tokens to the user. 

But, the user can choose to do a Fast exit if he wants to get hold of the tokens without waiting for the 7 day period. This is where the fast exit contract comes into play. It is expected that there is a token liquidity provider on the ethereum chain already. So the user who holds the exit NFT token can exchange it with the liquidity provider. The liquidity provider becomes the new owner of the Exit NFT and the user gets the corresponding amount of tokens after a small fees is deducted from it. 

The fast exit contract thus provides a mechanism through which the tokens can be obtained instantly. The liquidity provider shall then wait for the 7 days and can choose to use the exit NFT to get the actually withdrawn tokens.