The disciples remained near to Jesus as he was praying. That he should have broken off from his conversation with them and raised his soul with such solemnity and yet with such lightness to be with the Father and the Holy Spirit - for pure solemnity with any kind of heaviness would have broken off the intimacy with which he spoke to them - had probably become habitual and was regarded by them as normal. The elevated response of Peter to his question falls in completely with such a spiritual setting. Naturally in a divine mode Jesus knew exactly what the crowds thought of him and now he asked for a human account from them.
The disciples did not reply, 'Jesus, son of Joseph, the Nazareth carpenter.' Yet this was an easy question to answer, a factual question. The answers showed that the generality of the crowd regarded him as a prophet risen from the dead: even though Moses was a prophet (see Deuteronomy 34.10), the people had not made that identification. Rather that he was John the Baptist, or Elias who was regarded as the greatest of all the prophets: prophetic in his actions, not by any writings. Some did not identify him by name, but were impressed by his dignity with the additional thought that the earliest were the most fundamental, foundational prophets from whose example and inspiration the others had derived. Such was the judgement of the crowds.
Jesus then posed the more searching question to the disciples: 'Who do you say that I am?' It could have been an invitation to disclose their intimate thoughts, though perhaps it was a question about the way they spoke of Jesus to others, how they described him when they were away from the presence of Jesus, as the question had not arisen with such specificity among themselves. He was allowing them to be close to him, and to be inspired by the Holy Spirit about his identity Speaking in the name of them all, and, so it seems, instantaneously, Peter answered, 'The anointed - the Christ - of God!' That was an immediate identification with the Messiah.
This answer has a wide range and a narrow range, and probably includes both together as they were not in contradiction. The narrow range goes back to his baptism by John the Baptist when the Holy Spirit came upon his humanity about which John had spoken publicly: the reality of consecration, without the human ceremony, without the oil of consecration. He would be the realisation of the Messianic prophecy of Isaiah 11.
Debate about what it precisely entails is an affair of biblical scholars, but we could take some of their thoughts as expressing not all of the implications of the list of gifts of the Holy Spirit which the Christian Church has taken over and uses for the general activity of the Holy Spirit with his gifts: 'on him the spirit of the Lord rests, a spirit of wisdom and insight, a spirit of counsel and fortitude, a spirit of knowledge and of the fear of the Lord'.
Thinking that the Holy Spirit must always have diffused the same spiritual gifts, the Church sees Pentecost as an expansion of their activity, from being a present in individual historical figures to being gifts for all Christians as a multiple living principle of the spiritual reality of salvation: universal in its extent, and detailed in its actual working in individuals.
Jesus then turns the attention of the disciples to the fact that the anointed Messiah is also described by Isaiah as a Suffering Servant, and he details his future sufferings and death, and looks through them to his resurrection on the third day. And he opens their minds to the fact that not only is he the anointed of God, but 'the Son of Man': the divine presence discerned in a vision by the prophet Daniel at the right hand of the 'Ancient of Days'. The prophesy of Daniel was much read at the time, and the Marian part of Luke's 'Infancy Narrative' alludes to it. Amen.