This section of Mark's Gospel is actually very important structurally, as it forms the centre of the middle block of this Gospel before Jesus proceeds to Jerusalem. Coming thus at the literary heart of the Gospel it is vitally important that, having been with Jesus since the start of his ministry, the disciples have a chance to display how much they have been watching, listening, and above all understanding what Jesus has been doing and saying about himself. The question that you have quoted prompts Peter to give his firm declaration about the identity of Jesus. Note how he responds in Mark 8:29:
Peter answered, "You are the Christ."
He is the one disciple who is able to see past all the rumours and speculation surrounding Jesus to be able to defiantely state his belief that Jesus is the Messiah, the Christ, the long awaited Son of God sent to save God's people. This episode also signals a transition in the teaching that he gives to his disciples. After Peter's declaration, he begins to talk a lot more about the exact nature of what he will suffer in Mark 8:31 and onwards, giving rise to one of the most powerful verses in this gospel:
"If anyone would come after me, he must deny himself and take up his cross and follow me." (Mark 8:34)
Thus the question you have quoted marks a crucial transition in the Gospel of Mark and indicates the increasing understanding of at least one of the disciples as to the identity and purpose of Jesus.