Message signing is useful whenever you want to prove someone to be in possession of the keys associated with a certain address. Some exchanges require you to do such operation before enabling you to withdraw from the exchange onto such address. They will provide you a message template including some code or ID that will allow them to be compliant with their local regulation regime.
Note: Message signing is only available for singlesig accounts.
1.
Navigate to Receive -> More Options -> List of Addresses
2.
Find the address you will need to authenticate (or sign) a message with, then tap on the Sign icon
3.
Write or paste the message you need to authenticate (or sign) and then copy the signature to clipboard and share the signature with the counterpart requesting you to sign the message.