Off-the-record conversations for the Internet
With mathematical deniability, even if your chat buddy records the conversation, third parties cannot mathematically prove that it was you doing the chatting. This is of limited practicality for legal purposes unless you use OTR via an onion router or similar: otherwise there is enough associated log data to prove Bob's identity in court even if mathematically it could be forged. Even an onion router won't save you if you leave identifying information in the actual conversation and your chat buddy records the conversation. This is because the laws of evidence typically put the burden of proving that such recorded data was forged on the person it is being used against. Nevertheless, in the normal course of operations presumably OTR lives up to its name and does not record the conversation, and your chat buddy would have to go way out of his way to make it do so.
Of more practical use is the forward secrecy, which means that if your chat today is recorded by a third party in the encrypted form over which it is sent across the Internet, and that third party discovers your chat key in the future, that key can't be used to compromise the recorded but encrypted message. "Forward secrecy" means the key you used was destroyed after use, (like on Mission Impossible but automatically instead of with the self-destruct sequence drama), and even if future key(s) are compromised they can't be used to reconstruct the current key, and thus can't be used to decipher the current chat session.
This presentation gives a good overview of the messaging software's rationale and the basics of how mathematically deniable authentication and forward secrecy work. It points out that the law endorses off-the-record phone conversations: normally and in most jurisdictions recording phone conversations without consent is illegal. Cryptography, for the limited problems it actually solves, is far more secure than the law.