That was the winning spelling bee word and as it's a musical term I happen to know it (and how to spell it), which is pretty rare for me. Usually I've never heard of any of those words. So, I must tell you that, though the precise meaning can change a bit with the context and there's slight disagreements over when it does or doesn't apply, news reports have a pretty unsatisfying (to be charitable) definition. Appoggiatura is not simply another word for "melodic tone." That would be pretty boring. It is in fact a fairly precise kind of melodic tone, one that is non-harmonic (i.e., is not a tone in the chord of the underlying harmony) and is approached by a leap (or by nothing), and is resolved by a step. Almost always, appoggiaturas occur in accented places, metrically, and are a step above their ultimate resolution (grace notes and other embellishments are often appoggiaturas).
The example that's unfortunately coming to mind is the annoying song from Annie, "Tomorrow." In the chorus, (with some room for argument depending on the chords used) the second syllable of each 3-note utterance is an appoggiatura ["to-MOR-row"], on an accented beat, approached by a leap from "to-" and resolving down by a step into "-row." It is this sense of leaning down to a resolving note that gives it its name. The Italian word "appoggiare" is a verb meaning "lean on."
It really is shocking that this kind of fascinating tidbit doesn't help me get any dates, isn't it?