Why does Brown say that “There is no good on earth; and sin is but a name. Come, devil! for to thee is this world given” in the story?

This story is somewhat allegorical in nature, where Goodman Brown represents a sort of "everyman" Christian character (consider the Puritan honorary "Goodman" as ironic as well as "Brown" as quite a common name). Faith, his wife, represents Christian faith in general. Brown leaves her behind, opting to go into the woods—representative of committing sin—"one [last] night, [and then he'll] cling to her skirts and follow her to Heaven." However, faith isn't supposed to be something one has when it is convenient; Brown intentionally walks away from Faith, and this is his first step toward moral ruin.
In the woods, Brown repeatedly considers turning back and returning to Faith, but he never does. As he nears the Devil's meeting of sinners in the woods, he suddenly sees Faith's pink ribbon caught on a tree branch, and so he cries,

My Faith is gone! . . . There is no good on earth; and sin is but a name. Come, devil! for to thee is this world given.

With Faith gone, Brown feels that the earth is an evil place without goodness. The idea of being sinful is not a horror but, rather, a fact, a name only. He invites the Devil to him now, seeming to accept that the Devil and his evilness rule the world rather than God and his goodness. When Brown made the choice to abandon his Faith, he rendered himself unable to take comfort in Faith ever again. This is why, when he returns home, he turns away from her.

This quote is said at the point in the story where Young Goodman Brown has been shown that just about everybody he once thought a good Puritan Christian is actually in league with the devil. Just before Goodman Brown says this, he dreams that he hears Faith's voice. Then he sees something flutter down through the air. It turns out to be a pink ribbon. Brown assumes that it is the pink ribbon his wife wore in the first paragraph of the story.
Brown's faith in his wife and his Puritan community has been shattered, and his quote is a cry of desperation, anger, and acceptance all rolled into one. When he says that his faith is gone, he means that he has lost his wife to the devil; however, it also means that his actual faith in God and in his belief system has been destroyed. Brown is admitting that if those people are in league with the devil, there must not be any good left that the devil hasn't already tainted.