I remember this style of language from Little Red Riding Hood, a children's story in which the big bad wolf pretends to be a little girl's grandmother, while grandma is in his belly. When the little girl visiting grandma asks why she has such a big voice, he says "The better to greet you with!" She continues to ask a number of questions like this, eventually asking why grandma has such big teeth, to which the disguised wolf says "The better to eat you with!" and then he in fact eats her. :-). That's the only place I remember seeing that style of language. Note: In the version of this story I remember, no girl or grandmother was permanently hurt: the wolf was killed and both the girl and grandma recovered.

That's very weird English, but it basically means, "in order to [see his face] faster."