(1) Persuade, influence. (2) Bring about.
Example:
To induce him to make the call we had to promise we wouldn't do it again.
Inducing often refers to gentle persuasion -- inducing a friend to go to a concert, or inducing a child to stop crying, for instance. But an inducement may occasionally be a bit menacing, such as the Godfather's "Make him an offer he can't refuse." Induce also sometimes means "produce"; thus, doctors must at times induce labor in a pregnant woman. Induction often means the opposite of deduction, and is in fact closer to what Sherlock Holmes was actually doing.