Explain the concept of "incarnation" in this passage: "...One autumn night, five years before, they had been walking down the street when the...

The definition of an "incarnation" is when a god or deity becomes human.  So, this question implies that Gatsby is a god made human.  

There are elements in this quote from Chapter 6 that show Gatsby in an ethereal light.  For instance, the description of the moonlight shining and the mixture of darkness and seeing the stars.  The color "white" is also mentioned in this passage, which tends to be equated to purity and divinity.  

The last line of the passage is especially significant.  Only Gatsby sees this ladder that climbs upward, like toward heaven, and once he is there, all the wonders of the world will be revealed to him.  The last line gives the impression of omniscience to Gatsby, that he is as all-knowing as a god might be.

It is also significant that this passage takes place when he first meets and falls in love with Daisy.  The next paragraph reads:

His heart beat faster and faster as Daisy's white face came up to his own.  He knew that when he kissed this girl, and forever wed his unutterable visions to her perishable breath, his mind would never romp again like the mind of God.  So he waited, listening for a moment longer to the tuning-fork that had been struck upon a star.  Then he kissed her.  At his lips' touch she blossomed for him like a flower and the incarnation was complete.

This passage almost reads like the story of Adam and Eve--when they take a bite from the Tree of Knowledge, all is revealed to them in that moment, but it is also the start of their fall from grace.  So, too, will this kiss be the beginning of Gatsby's fall.