You can use this option to cross check your wallet's private keys to the wallet's receiving addresses. This checks the internal consistency of your wallet.
To check the private keys of a wallet, do the following:
In the "Wallets" side panel choose the wallet for which you want to check the private keys.
Select the menu option "Tools | Check Private Keys". The "Check Private Keys" screen appears.
If the wallet is password protected, enter the password in the "Wallet password" field.
To check the private keys for the wallet specified, click on the button "Check private keys". A message will appear upon completion.
If the check was successful your wallet is internally consistent and there is nothing more for you to do.
If the check was unsuccessful a note will appear telling you to read the Messages tab. In the Messages tab are details of which addresses do not have the correct private keys. You should not send any bitcoin to these addresses as it will not be redeemable.
Any existing balance on the addresses specified can only be redeemed by recovering the private keys. You should search your MultiBit Classic and Blockchain.info backup wallets and private key exports to find these private keys. You can then import them into your wallet of choice and recover your bitcoin.
If you have no copy of the relevant private keys in any backup then the bitcoin on these addresses will not be redeemable. At this point you should consider data recovery software if you think there is a chance that a deleted backup may contain a working private key.
If you have really, truly lost your private keys, then it is likely that you have lost access to your bitcoin. There is absolutely no way that the MultiBit team can possibly recover them.
You should keep the encrypted files safe just in case inspiration strikes. Never delete a wallet, just archive it safely.