Answer:
Swift's essay is a great example of the way that Augustan writers took on political and social issues. Swift was a big critic of English policy in Ireland, which, if you've read up on your history, you'll know was pretty freakin' brutal.
Here Swift is pointing out just how heartless and cruel the English were toward the Irish, and especially the poor Irish… which, let's face it, was most of the Irish. Hey, Swift is saying, you might as well just eat Irish babies, since you're ruining them, anyway.
Satire is the mode of this essay. Swift, of course, doesn't actually mean that we should all go off and eat Irish babies. He's being ironic. He's suggesting something so outrageous, so cruel, and so horrible that it's funny and scary all at once.
The point is, by deploying this satirical mode, Swift is reflecting back to his (English) readers their own cruelty toward the Irish. By making such an outrageous proposal (eating babies isn't "modest" by any stretch of the imagination, is it?), he's exposing the terrible treatment of the Irish.
Hope this helps!
xoxo,
cafeology