Can someone please explain to me what these two options in Multibit Client do?
When you sign a message you are essentially proving that you are in control of the private key of the address that you are signing from. The most common use of this is to verify that you in fact have sufficient funds to pay for a transaction. Other uses for this feature is to prove you are someone who participated in a particular transaction.
To verify a message is to verify that a signed message (see above) was in fact signed by a particular address.
