Jesus saw Nathanael coming toward him and said of him, "Behold, an Israelite indeed, in whom there is no deceit!" Nathanael said to him, "How do you know me?" Jesus answered him, "Before Philip called you, when you were under the fig tree, I saw you." Nathanael answered him, "Rabbi, you are the Son of God! You are the King of Israel!" Jesus answered him, "Because I said to you, 'I saw you under the fig tree,' do you believe? You will see greater things than these." And he said to him, "Truly, truly, I say to you, you will see heaven opened, and the angels of God ascending and descending on the Son of Man."-John 1:47-51 ESV, emphasis mine
As I listened to the passage, it occurred to me that Jesus, who was operating in His capacity as Man, had received a vision of Nathanael by the Holy Spirit, Who had descended on Him at His baptism earlier in the chapter. Then Jesus told Nathanael that he would "see greater things than these." It's interesting how Jesus' statement is broken up at the beginning of verse 51, "And he said to him..." as though Jesus were making a separate statement. I always assumed that Jesus meant that the "greater things" were the same thing as "heaven opened, and the angels of God ascending and descending on the Son of Man," but to me the way the sentences are written leaves that open to another interpretation.
This chapter, in my ESV, contains the word "see," "seen," or "saw" fifteen times, beginning with the idea in verses 14-18 that although no one has seen the Father, we have seen Jesus and thus have seen God's glory. Then we find out what John saw, what Jesus' soon-to-be disciples saw, then what Jesus saw. And when Jesus saw something, He immediately said that Nathanael would one day "see" greater things. It's almost like the point of Chapter 1 is to emphasize that God purposefully reveals things to people. Maybe Jesus was speaking of the day when His disciples would also be filled with the Holy Spirit and would be able to see prophetic visions like Jesus did (see Acts 2:17 and Joel 2:28). "Do you believe I am the Messiah because of a little vision? Even YOU will see visions one day!" Jesus seems to be saying. Receiving prophetic visions, apparently, is not a valid sign that you are the Son of God!
So what is the significance of verse 51? I looked it up in Matthew Henry, and his explanation is that Jesus meant that Nathanael would see more valid indicators that Jesus was the Messiah, which also makes plausible sense in context. I think there is a little mystery left there, a little bit of ambiguity. Maybe Jesus meant a little of both... that Nathanael would see valid indicators of His Messiahship, and also that Nathanael would one day see and understand things by the Holy Spirit. After all, Peter did, even before the Holy Spirit was given.