。
Won't you come to our house for dinner?
Literal
Dinner [to-に] house [to-へ] come-[honorific-いらっしゃいませんか]?
いらっしゃる is the honorific catch-all verb for 行く/来る/いる — it elevates the listener's motion or existence. The negative-invitation form いらっしゃいませんか is a courteous 'won't you come?' — far more polite than 来ませんか. Compare usage across politeness levels: 来る → 来ませんか → お越しになりませんか → いらっしゃいませんか.