First things first. Sgt Pepper is not a concept or themed album. 3 of the 13 songs are vaguely based on the theme of the Beatles "playing" at being an old time band (including a reprise of the title song) and some of the music is continuous between songs. The rest of the songs are unrelated so why is the album so often described as groundbreaking? Listen to it and you will find out. The band and producer George Martin produced a remarkable album that at times is unashamedly experimental.
It is probably best summed up in "A Day in the Life", where they really throw the kitchen sink at it. In the middle and at the end of the song an orchestra builds a wall of sound for what seems like forever, until a crescendo is reached. It sounds remarkable now, it must have blown minds when it was released. And all this from songwriters in their twenties, though undoubtedly greatly influenced and encouraged by Martin.
"She's Leaving Home" deserves special mention. The lyrics beautifully describe the angst felt by a teenager who feels she has been "living alone" with her parents for too long. Along with the gorgeous music this song never fails to resonate with me.
"When I'm 64" shows Paul at his most playful music wise but again the lyrics are spot on. John contributes the classic "Lucy in the Sky with Diamonds". George demonstrates his experimental work with Indian music in "Within You Without You".
And I haven't even mentioned "With a Little Help from my Friends" and the title song, both classics in their own right.
Not every song is a classic. "Getting Better" and "Fixing a Hole" aren't up to the standard of the more famous songs though they do show how willing the band were to try new things, especially lyrically.
The best Beatles album? Quite possibly. I never tire of listening to it.