Sgt. Pepper's Lonely Hearts Club Band, by the
Beatles, is widely regarded as the first concept album. Instead of an album being a collection of songs, the
Beatles wrote the songs as if they were a different band, with different members and style.
The concept album is a pretty loose term. On the most concrete end are albums like DJ Qbert's Wave Twisters, or Pedro the Lion's Winners Never Quit, where the album tells a definite story which makes little sense if heard out of order. On the other end are albums like Sgt. Pepper, where there is a theme running throughout the songs but the album could still make thematic sense if listened to on shuffle.
I'd argue that this was the most significant (and perhaps only important) influence the Beatles had on rock music.