Ideas from Rob Bell's book, "Velvet Elvis":
As mentioned in previous posts, ancient rabbis had different rules applying their understanding of the scriptures. These interpretations were referred to as a rabbi's yoke, and a student of the rabbi was said to have taken the yoke of that rabbi.
Very rarely, a rabbi would arrive on the scene with a new interpretation of the Scriptures. This was nearly unheard of; after all, the scriptures had been debated and studied for centuries; how is it some newcomer has more understanding than all his predecessors?
So when this happened, the new rabbi was often challenged on his authority.
Jesus came along and said things like, "You have heard it said that X, but I tell you Y". He's essentially saying that other rabbis have it wrong; this is the correct interpretation.
The existing power structure challenged him with "Where did you get your authority?"
And Jesus' usual response was "You tell me, where did John get his?"
Jesus' appeal to John's authority was important, because in the case of a new rabbi coming along with a new yoke, it was a protection to him if two other rabbis laid their hands on him, essentially validating him, witnessing to their belief that the new rabbi had such authority to teach a new yoke. John, who was an important rabbi in that area, had made just such a witness to Jesus, saying that he was not worthy to untie Jesus' sandals.
John was one of the two necessary witnesses to Jesus' authority to teach a new interpretation of the Scriptures.
The second witness came just after Jesus came up out of the waters of immersion, when a voice from heaven proclaimed, "This is my beloved Son, in whom I am well pleased." (Later, on the Mount of Transfiguration, the phrase "Listen to him!" was added during a second endorsement by the voice from heaven.)