At the beginning of The Great Gatsby, Nick notes how his father taught him to appreciate the advantages he's had and that others may not have had those advantages. Nick intuits that his father meant much more than that, so Nick decides that he will be open-minded and "inclined to reserve all judgments" (Chapter 1). Because Nick claims that he goes about his life open-minded and reserving judgment, he is quite serious and consistent in this approach to life and therefore, he is honest in that he honestly tries not to judge anyone.
As the novel progresses, Nick engages with people at Gatsby's parties, Daisy, Jordan, and Gatsby himself. Among many of these people, Nick observes superficiality and blatant dishonesty. Tom cheats on Daisy. Daisy eventually cheats on Tom. And although Nick has an affinity for Gatsby's idealism, Gatsby's persona is an illusion. Nick observes the people at Gatsby's parties, thinking they are just using him for the place of a social gathering. This becomes apparent when Nick discovers that most of the guests know next to nothing about Gatsby. Of Jordan Baker, Nick says:
She was incurably dishonest. She wasn't able to endure being at a disadvantage and, given this unwillingness, I suppose she had begun dealing in subterfuges when she was very young in order to keep that cool, insolent smile turned to the world and yet satisfy the demands of her hard, jaunty body.
Nick consider himself honest from the outset. But as a young man from a Midwestern town encountering such superficial elitists in the city, he considered himself even more honest by comparison.