Not every album is a song cycle or designed to be listened to as a complete work of art. But the songs were more or less recorded in the same time frame, and someone tried to create a musical flow, from one song to the next.
Some musicologists cite Frank Sinatra's 1958 album, "Only the Lonely," as the first "concept" album, for its sustained theme of late-night moods and melancholy. There were probably earlier pop song cycles, but it was definitely the Beatles' "Sgt Pepper" and the Who's "Tommy" that thrust the concept album into mainstream tastes. That was a long time ago, but albums as collections of songs are still being made and sold across all genres of music. Radiohead's "Kid A," Arcade Fire's "Neon Bible," and Beck's "Sea Change" demonstrate the relevance of albums in our time.
In the LP era, before the CD format was introduced, songs were divided between Side 1 and Side 2. LP playing times maxed out around 50 minutes, but 17 to 22 minute sides were the most common durations. Side 1 and Side 2 might have very different musical personalities, and there were lots of records where I favored one side over the other, or just played one side. LPs are still coming out, but the primary album medium is CD, so I don't think the old Side 1, Side 2 distinctions are relevant anymore.
Even with LPs some listeners jumped around from one song to another, or flipped the record over to play a favorite tune. But most of us played complete sides, and sometimes through repetition fell in love with songs that didn't at first seem all that interesting. That was part of the beauty of the format, and if the band was good, there was at least a fair chance you'd enjoy most of the songs. That's far less likely to happen now, either because people just get the songs they like, or they just listen in shuffle mode. Those listeners may never discover the real gems from their favorite artists.
I've heard from a lot of people who regularly listen to albums all the way through, so it's not that it never happens anymore, just less and less. Most music buyers purchase individual songs, but as streaming services like Spotify and Pandora continue to attract more and more subscribers, fewer and fewer folks will be listening to albums. So why would record companies or individual bands spend money and expend the effort to record 10 songs if they only sell two or three of them? The bands will, probably sooner than later, stop making albums.