Wikipedia (currently) describes the core genre elements of pop music as follows:
Identifying factors include generally short to medium-length songs written in a basic format (often the verse-chorus structure) as well as the common employment of repeated choruses, melodic tunes, and hooks.
It's usually distinguished by a certain direct simplicity, structurally speaking. It can be quite ornate and ornamented, but the underlying focus is squarely on hitting those audio pleasure centers. It generally doesn't make its audience "work" as hard, or be as musically educated as more challenging genres. It's probably fair to say it overlaps with all genres --there are pop versions of nearly every style of music. One of the most reliable recipes for a hit is to record a pop song in a fringe genre.
There can definitely be unpopular pop music --some of my favorite artists have made a whole career of "pop" songs that never hit the charts. And some music that defies categorization as "pop" can become immensely popular. As far as whether the genre predated the term --arguably. There exist classical compositions, and songs from other ancient traditions that bear many of the hallmarks listed above. As far as whether it waxes and wanes --definitely. The 50's, 80's and early 2000's are all noted for the dominance of a pop aesthetic, while the 60's, 70's, 90's (and arguably today) all featured something of a pop backlash --although of course, it's a mix in every era.