A man-in-the-middle attack is possible because of the nature of the Internet and the popularity of public key crypto. It involves intercepting the messages and masquerading as the parties concerned.
Theoretically, the man-in-the-middle (MITM) could block a message from Alice to Bob. He could then masquerade as Bob to Alice, and as Alice to Bob. Without proper authentication (see digital certificates) this could be possible. MITM could receive and read messages from Alice before sending them on the Bob (and vice versa).
If MITM never alters the messages, Alice and Bob may never know that their messages are being intercepted.