Nick realizes, when he sees the way Jay and Daisy look at one another and when he feels the nervous, awkwardness of the meeting between these two for the first time in almost five years, that his presence is not necessary nor is it wanted. Nick has good intuition about people because he tends, as he tells the reader in the first chapter, to listen to people, rather than judge them. Nick is also somewhat stricter morally than either Daisy or Jay (or many of the characters in the story) and it is embarrassing to him because he knows that an affair will take place between the Daisy and Jay. He tells the reader at the end of the novel that one of the reasons he moved back to the midwest was because he was tired of the immorality of the people in the east. Also, Nick is too polite and too much the gentleman to eavesdrop or interfere in someone else's business. This scene helps to emphasize Nick's moral character.
Nick's house is just a neutral location for Gatsby and Daisy's reunion; he himself really plays no role. Their conversation, he believes, is private, and he is embarrassed by the obviously strong memories and feelings shared by the pair. Leaving them alone seems to be his best choice, but where is he to go? It's Nick's house; he apparently believes his only option is to withdraw from the house to the outside where he walks around to pass the time, allowing the couple ample opportunity for private conversation. Nick has had no experience with this kind of social interaction; he feels awkward, like the proverbial odd man out.