Rigoletto hears the Duke whistling this aria's melody from offstage as he prepares to dump the Duke's shrouded body into the river -- and discovers that the body the assassin gave him is instead that of his own daughter, Gilda.
The music is so memorable that Verdi reportedly refused to allow the tenor to see the score much in advance of the opening night -- he didn't want the gondoliers singing the melody before the opera's premiere. See for yourself, at http://www.amazon.com/exec/obidos/clipserve/B0000042HZ001012/002-0767511-0401638

The aria is, of course, deeply ironic, because while claiming "woman is fickle" the Duke has already demonstrated his own fickleness (and boasted about it in the first act's Questa o quella -- "This woman or that one, they're all the same to me"). This is not a morality play, though, so the Duke is never called to task for his infidelity.