Gatsby displays nervousness as chapter 5 opens, and Nick returns home. Gatsby has had Nick's lawn mowed because he wants everything to be perfect for Daisy's arrival, which is also why he has a "greenhouse" worth of flowers sent to Nick's house. He wants to exert as much control over this situation as he possibly can.
Gatsby is usually cool and collected, so his nervousness betrays how important this meeting is to him. It is the culmination of all his dreams over the last five years. Finally, he is going to once again see the woman he has loved and who has dominated his thinking and given his life its focus ever since he left her.
Gatsby, at two minutes to four, despairs, thinking Daisy has stood him up, though she is not due until four. This shows that not only is he nervous—he can hardly allow himself to believe this is happening.
When she comes, Gatsby continues to be uncharacteristically nervous and Nick has to scold him in the kitchen and inform him that Daisy is embarrassed and needs to be set at ease. This jolts Gatsby out of his focus on himself and his own emotions and towards thinking about her.
Gatsby wants to take Daisy to see his house as part of his carefully choreographed plan to first meet with her at Nick's before impressing her with the wealth and grandeur of his life. Nick never explains why Gatsby wants him to come tour the mansion too, but we could surmise that Nick's presence helps Gatsby stay steady and calms his nerves. Gatsby may not yet be ready for the feelings the might overcome him were he to be alone with Daisy. The meeting is already almost more than Gatsby can bear in his emotional state, but nevertheless it succeeds.
Yet as Nick notes, it is impossible for Daisy to live up entirely to Gatsby's dream. Nick states:
There must have been moments even that afternoon when Daisy tumbled short of his dreams—not through her own fault, but because of the colossal vitality of his illusion.
Gatsby, unfortunately, for all his efforts, can never meet the standards of Tom and Daisy's upper-class world because he did not grow up in it. For all his wealth, he is always nouveau riche, never quite able to make it in their old-money society.