As language evolves, some words widen in scope while other words narrow. "Girl," for example, used to mean a child of either sex. To put it another way, a word can come to apply to a subset or a superset of the set it originally applied to. I can't remember the "sexy" linguistic term(s) for this kind of change. (It's kind of a pet peeve of mine when people use "sexy" to basically mean technical. Isn't it just an excuse to say "sexy," suggesting that you either are sexy or are particularly tuned in to sexiness?) This is a different process from words becoming pejorative (less positive), the way "fine" used to mean lovely or excellent and now just means okay, or "handicapped" became an insult.
I think the term "emo" is widening in scope. When I first heard this term it referred to a very specific genre of music (an example of which is Sunny Day Real Estate). Now it seems to refer to anything or anybody that is emotional or associated with emotions. I heard someone refer to an upbeat pop song by Regina Spektor as "emo" on Twitter yesterday. Long bangs? Emo. Using the hood on your hoodie? Emo. I feel alienated from people who use the word "emo" in this way, probably similar to how my parents feel about my generation's use of the word "awesome."
What's a term that is currently narrowing in scope? Like it seems to be applicable in fewer situations than it was earlier in your lifetime? I'm having trouble thinking of one. You could probably do this exercise just with music genres, but I don't know enough about them.