What is the effect of the word modest in the title?

There is nothing "modest" about Swifts proposal. Eating babies is part of it, which, although satirical, makes the title ironic. The entirety of “A Modest Proposal” is satirical because it makes fun of other grand ideas that people have proposed to solve big problems in society. The proposal itself—that the Irish should eat their babies—is satirical, too, because it makes fun of people who propose absurd things thinking that they are practical.