It started back in the days when that "other band" was barely acknowledged and many people didn't even know what FM radio was. So stations that made the investment in the early 60s often just simulcasted their AM programming as a placeholder on the other band. 

But in 1965, the FCC in the U.S. ruled that was illegal and that owners would have to properly program their twin on FM. With nothing to fill all that time, things morphed into the format so many remember.

"A blend of soul, blues, jazz and world music began to take over the music stations, but given the popularity of rock ‘n’ roll at the time, rock music reigned over the airwaves.

The mid-60s gave way to the counterculture, which was soundtracked by bands gaining cult followings through performing live and releasing records, but they rarely got played on AM radio’s’ top 40 stations, so they became known as ‘underground’ artists, as did the FM radio stations that were playing their music.

"Of the DJs who reigned over FM radio, many of them chose to play not only the artists’ singles, but album tracks, as well, leading to the advent of album-oriented radio."

The simple 1965 FCC ruling that led to the rise of the album