Just as most of the cathedrals we can visit in the United Kingdom have an area called the cloisters, so also the great Temple in Jerusalem had this area which was used for discussing the great theological issues of the day. Rabbis would stroll in that shelter to teach and to answer the questions of their disciples. So, as Jesus walked and talked, a delegation from the chief priests and religious leaders came to set what they considered profound questions to Him to destroy Him in debate.
Their plan was to put Jesus in a dilemma: if He answered their question by saying that He was acting under His own authority then they could be justified in arresting Him as a megalomaniac. However, if He said that He was under the authority of God, then they could arrest Him for blasphemy, as surely God would never authorise any person to cause such disturbances in His house.
Jesus was far too clever to be caught in their shenanigans and He answered their question with a question of His own, an oft used device by Him. He asked them what authority John the Baptist had when he baptised. Was it from God or from man? An unanswerable question, as to say that John was speaking words and doing things under God's authority would entail admitting that John's words about Jesus must be true. But to say that all he did and said were entirely from him was to cause a sensation amongst the crowds there. Remember that he had been executed by Herod, so he was a martyr to most if not all Jews.
This whole incident reminds us of what happens to those who will not face the truth. Those who are committed to the truth may have to apologise at times for getting things wrong, but it does mean that their word is trustworthy and everyone can assume that the truth is their intention, rather than political gain.