This quote, from Act II, scene iii, is a great one to choose in discussing Benedick, since it is short and deceptively simple. Not only does Shakespeare pack a good dose of information about Benedick in these few words, but he also manages to make reference to the play's title (which would have, in the pronunciation of English in Shakespeare's day, sounded like Much Ado About Noting, or "seeing").
The line you quote is part of an extended soliloquy in which Benedick expresses his distaste for love and the men who allow themselves to fall into it. The soliloquy is in prose, which is odd for a soliloquy (usually written in verse) and hints at the fact that here, Benedick may not be speaking the complete truth, that he is "putting on" for the audience rather than speaking from his heart.
Here is your quote, in context:
I do much wonder that one man, seeing how much another man is a fool when he dedicates his behaviours to love, will, after he hath laughed at such shallow follies in others, become the argument of his own scorn by falling in love: and such a man is Claudio.. . .May I be so converted and see with these eyes? I cannot tell; I think not.
These words are important because Benedick will become the exact same "turncoat" to love that he accuses Claudio of in this soliloquy. Claudio used to make fun of men who fell in love, and he, himself, has fallen in love. And though Benedick says he "thinks" he will "not" do the same, it will be shown in this very scene that he allows himself to fall "in love" with Beatrice.
So, Benedick will be converted, but "seeing" is both a literal and figurative thing. And Benedick will "see" his friend Claudio with different eyes once he commits himself to love of Beatrice. He will challenge Claudio to a duel for defaming Hero. No longer will Benedick "see" the world as one big joke, but for Beatrice's sake, he will act the part of a hero and "see"the seriousness of life.
Benedick, as he mentions in the quote, will not "see with these [same] eyes" once he is "converted" by love, but will rather, "see" the world in a new light for the sake of the woman he loves.
For more on "seeing," and Benedick in Much Ado, please follow the links below.