"A Modest Proposal" is one of the more famous satirical essays of all time. In response to a famine, Swift is jokingly suggesting that people start eating children. The ironic tone used is meant to draw attention to how callous and ridiculous some of the proposed solutions to this famine were. If you thought of it like a modern dialogue, it would be something like:
Government: This famine is getting out of control. All of these hungry people have become such a burden unto our country.
Swift: Oh, no, I definitely see your point. How about we just start eating them, then? If they're such a burden, I mean.
He's obviously not being serious, but rather trying to mock other people.