Back when Jesus walked the earth, there was a lot of speculation as to who he was. As indicated in this passage, some thought He was John the Baptist, some said Elijah, others said one of the prophets (Mark 8:28). If you're looking for indications that the Bible advocates any notion of reincarnation, this is about as close as you'll get. Really, they were probably thinking in terms of Jesus being one of these great prophets risen from the dead.
But Peter - and likely most of the other disciples - knew who He really was: "You are the Christ" (Mark 8:29).
That's all gospel writer Mark has to say about it. But turn back to Matthew 16:17-19 and you'll gain a lot more insight! Peter was not a Pharisee or a Scribe, not learned in the scriptures. Peter was a fisherman. The Jewish leaders of the day, with all their knowledge, didn't recognize Jesus as Messiah. But this simple fisherman did.
In the Matthew passage, Jesus says something vital to Christian doctrine: "This was not revealed to you by man, but by My Father in heaven." So all the book smarts in the world won't reveal this vital truth to you; all the experiences of life won't help you. Only the Heavenly Father can reveal this to you.
I've read books by brilliant Bible expositors, studied doctrine and philosophy. I don't understand most of it, and couldn't begin to explain most of the concepts. But one thing I do understand is when these speakers and authors simply state - confess - Jesus Christ as Messiah. Unlike the Pharisees, they've overcome their vast knowledge and humbled themselves so that the Heavenly Father could reveal to them His Son, sent to redeem the world from sin.
Jesus continues in Matthew 16:18 that Peter's humble confession - impossible to know without divine revelation - was the basis on which the church would be built. And today that prophesy is seen in churches around the world which all share the premise of being built upon the humble confession revealed by God.
Will you humble yourself today and allow God to reveal to you His Son?