This passage is at the tail end of a paragraph describing Gatsby's appearance and clothes right before Daisy comes to lunch. He has not seen Daisy since the Great War, so he wants to make a great impression. He dresses in a flashy style (white flannel suit, silver shirt, and gold tie) to emphasize his wealth and prove he is no longer the poor boy she once knew and stopped waiting for all those years ago. However, the sentence describing his pale complexion and baggy eyes betrays Gatsby's nerves about seeing his dream woman after so long.
The juxtaposition between Gatsby's clothes and his tired face do well in showing how Gatsby still feels inadequate despite all of the money he's accumulated. Gatsby and Daisy might both be wealthy now, but he still lacks the breeding and manners that come with being from so-called "old money" as Daisy is. His clothes emphasize this element, since new money is often associated with poor taste in fashion (overcompensating through bold colors, for instance). Gatsby's initial poor manners and obvious embarrassment when Daisy finally appears also betray his lack of social decorum.
So, this passage does more than describe Gatsby's appearance or even his feelings: it reveals just how insecure he still is about his social class.