We love your children very much, but we want you to have the evening off to celebrate with us, so the reception is adult-only.
If your invitation was addressed to you "and guest," then feel free to bring someone special. If not, we'd prefer it if it were just you.
"Black tie" means tuxedos for the men and gowns for the ladies. If you're not feeling that fancy, a suit or a classy cocktail dress will be fine.