Message Authentication Codes

Suppose Alice and Bob share a MAC key, and Bob receives a message with a correct MAC using that key.

Then Bob can be assured that Alice is the one who sent that message, and that it hasn't been modified since she sent it!
This is like a "signature" on the message.
But it's not quite good enough!
Bob can't show that signature to Carol to prove Alice sent the message.
Alice can just claim that Bob made up the message, and calculated the MAC himself.
This is called repudiation, and we usually want to avoid it.