The speaker describes the problem of poverty in Ireland, which he attributes to the lack of opportunities to earn money. He writes of mothers, trailed by hungry children, forced to beg for food, and of people forced either to steal or to sell themselves into slavery or as mercenary soldiers in foreign countries so that they will not starve. The narrator characterizes this as a "deplorable state," and notes that the person who could find a reasonable way for the children of the poor to earn money would deserve to have a statue in a public square.
From the speaker's tone and the way he raises the reader's emotions of pity and empathy in his descriptions of the plight of the poor, the reader is led to expect a compassionate proposal to solve the problem of poverty, only to be all the more surprised later in the essay when the narrator's idea is to butcher poor one-year-olds as delicacies to be eaten by the rich. It's also worth noting that the speaker, although he calls his proposal "modest," seems to think a statue should be erected to him for such a "fine" solution to the problem of poverty. It's important to remember that this speaker is not Swift, the author of the piece, but a clueless bean counter, and that Swift expects us to be horrified by his ideas.