My understanding of Swift's "A Modest Proposal," is that he is looks for a way to deal with Ireland's poverty. In doing so, he directly refers to the growing birth rate, where too many children are produced to be able employ, either honestly or of an unlawful nature.
The entire essay is an example of harsh satire: Swift suggests that instead of watching the Irish bear children who will ultimately starve or turn to a life of crime, other steps be taken to address the issue. "Satire" is holding up an idea or perception to ridicule, and can be done in a "mellow" or "harsh" light.
Dr. L. Kip Wheeler describes satire as:
An attack on or criticism of any stupidity or vice in the form of scathing humor, or a critique of what the author sees as dangerous religious, political, moral, or social standards...
Though born in Ireland, Swift's early years were spent in England, and he moved between both locations, ultimately carving out a spot for himself within the Protestant church of Ireland. However, he had a strong voice, offering his displeasure of political events and social issues, both in Ireland and England.
In the case of "A Modest Proposal," Swift was dismayed by poverty in Ireland. It is suggested that the essay (pamphlet)...
...suggests ironically that the English might as well eat Irish babies since [the English] are already devouring the country economically.*
Swift's general concern was that of starvation and poverty: that point stands firm regardless of the satirical essence of the piece. The satire is evident when he, with great sarcasm, suggests that the problem would be solved if people would simply eat the children when young which would be better for everyone around. This is, of course, NOT what he was literally suggested, but simply an outrageous suggestion to gain attention from the British government to address the problem. It has been noted that the piece fell short of its mark: Swift's audience did not "get" the satirical intent of the piece.
*Source: Adventures In English Literature. Orlando: Harcourt Brace Jovanovich, Publishers, 1985.