There are some differences of opinion on this. The name "Gudakesha" is applied to Arjuna in the Bhagavad-Gita, and some take this to mean "master of sleep." In this interpretation, it refers not to some event, but to his friendship with Krishna or because he has a vision of Krishna as God. In this case, "sleep" is a metaphor for "ignorance." So the implication is that because of his knowledge of Krishna, he has overcome ignorance and sees through the illusion of the world.
However, an alternate interpretation suggests that "Gudakesha" simply means "Thick-haired" as defined in Monier Williams Sanskrit Dictionary. In this interpretation, Arjuna is not the "master of sleep" but simple "think haired."
Generally, the sources that describe Arjuna as the "master of sleep" are Vaishnava devotees to Krishna such as ISKCON (International Society for Krishna CONsciousness). I've put a link to one of these interpretations below. The second link is a page from an online version of the Monier-Williams Sanskrit dictionary.