7:14
Jesus chose the time to go public. All the events surrounding Jesus’ life are under God’s control, including, indeed especially, the events surrounding Easter (which are still several months away). Jesus went to the temple and began to teach. Teaching was central to Jesus’ ministry (see e.g. Mark 1:21, 1:38; 3:14; 6:30). The people need to hear Jesus’ teaching because without it we do not know the truth.
7:15,16
The Jews marvelled at Him. Given the earlier distinction between the Jews and the people (7:11 and 12) I think we have to take this as referring to the Jewish leaders and teachers. They were amazed that Jesus could teach with authority and learning. Clearly He came across as knowing what He was talking about. Unlike other rabbis, Jesus had never studied at the equivalent of a divinity college, yet He knew so much! Now it is good to go to Bible School, but it is not essential. A respect for God’s word is far more important than academic learning, but academic learning linked with a fear of the Lord is a powerful thing.
Jesus explained why He was able to teach with authority and knowledge. His teaching came from the One who had sent Him, ie from the Father. The rabbis of the time would frequently quote other rabbis for what they said, thus claiming authority from earlier rabbis. So the concept of your teaching not being your own was well established, and if someone was teaching purely on their own authority they would be dismissed as irrelevant. Jesus had the best teacher of all, His Father.