MOR used to mean American Songbook or Standards, along with Broadway show tunes. As Gregg said, it was pop artists like Sinatra, Nat King Cole, Andy Williams, Dionne Warwick, Patti Page, Steve and Eydie, etc. MOR tends to include ballads, but not rock n' roll or country. So if a typically rock act recorded a ballad, it might be played, but not the rock act's rock songs. An example might be "Let It Be", a ballad from the Beatles. But Beatles' rock music would not be played.
The most popular MOR station I can think of was KMPC 710 in L.A. Another station was KGIL, who covered the San Fernando Valley, but their transmission range wasn't very far. I don't think they reached Pasadena or Orange County.
I used to think that MOR stations were "lame", because my parents listened to them. But they could have cool DJ's. Wink at KMPC used to talk about his friendship w/ Elvis in Memphis; and even though Elvis was really not part of their format, sometimes he played Elvis ballads.
Wink used to talk about record producers, like how Jimmy Bowen produced songs for Sinatra ( on Capitol Records, I think), and that was very interesting.
Johnny Magnus was on KMPC at night, and he talked about standards tunes as if they were very jazzy and hip. Johnny used to do a feature called "Weather With a Beat", where he gave temps and weather conditions around the nation to a Count Basie song, I think.
He had a very ethereal, mellow kind of a voice. I used to lie in the dark with my radio under my pillow, think of all the far away towns with their buildings lighted up in the still of the night, and what fun it would be to travel there.
MOR stations can succeed with age 18-34 demographic, but it depends on the DJ. It needs a "with it" DJ who really can interpret those records, artists, songwriters, and producers.
I'm sure that someone will show up at any minute and grumpily, angrily, debunk everything I just wrote.
That's okay. I still liked KMPC and KGIL.