Most of us think in terms of music genre like rock, metal, funk, R&B etc but there are patterns to these that transcend their genres and it turns out that understanding those patterns you can recommend music for someone they will enjoy even though it is outside their normal genre.
Like the song Come On Eileen sounds like a very original song, and it is, until you look at it in terms of structure, the way it switches keys, "common tone and diatonic pivot modulation" (heh) and then from that point of view it turns out to be just one of a great many similar songs. So you like that song, Pandora (or whatever) can recommend a lot of similar, and yet at the same time very different, songs.
That is the positive aspect. The commercial and very negative side is they can also look at sounds and patterns people tend to like and come up with lots of music that has a lot of mass appeal even though it is really drab repetitive mindless soul-sapping dreck. Like, the ooh-wa-ooh. Hard to type or read but when you hear it you will realize it is everywhere. Turns out something like 75% of all the hits across seemingly very different genres were written by the same two guys. Sounds impossible but true. Go find the YouTube video and check it out.
Unfortunately none of that seems to work very well for me. The few times I come across new music that I really like it inevitably turns out to be too poorly recorded to want to buy. Because I am fussy and only get the good stuff now. But the way they're able to analyze and systematize something that to me seems impossibly complex, well that is just totally fascinating to me.