Not only does "Imagine" possess some of the simplest lyrics in rock music, but it also was written in the most basic key, C Major. But just like"Lean on Me," "Do-Re-Mi," "Heart and Soul," and "Have You Ever Seen the Rain," "Imagine" proves that C Major is one of the most feel-good, enduring keys that exist on piano.
Speaking of which, Lennon has said in many interviews that he's no good on the piano. He once said, "My piano playing is even worse than me guitar. I hardly know what the chords are, so it's good to have a slightly limited palette." (Source)
"Imagine" remains one of Lennon's few solo masterpieces composed solely on the keys (the strings that back him up in the final track are not his doing). In his 1970 Rolling Stone interview with Jann Wenner, Lennon remarked that he was gearing up to get back to the basics. He'd had enough of tricky melodies and complicated harmonies that marked songs like "I Am the Walrus," and wanted to return to the core of the music:
Well, I've always liked simple rock… I always liked simple rock and nothing else. I was influenced by acid and got psychedelic, like the whole generation, but really, I like rock and roll and I express myself best in rock. I had a few ideas to do this with "Mother" and that with "Mother" but when you just hear, the piano does it all for you, your mind can do the rest. I think the backings on mine are as complicated as the backings on any record you've ever heard, if you've got an ear. (Source)
As far as time signature and rhythm go, "Imagine" also happens to be written in the most regular, even beat that exists in music: 4/4. That just means that there are four beats to every measure and a quarter note (1/4 of a second) receives one beat. Essentially, each measure of music comprises an entire second and it's the steadiest, most recognizable, most natural form of meter. Just as Shakespeare discovered that the iambic pentameter rhyme scheme in poetry most closely mimicked the rhythms of natural English speech (and the human heartbeat), so too did musicians understand that 4/4 was their innate beat.
As Yoko, who was classically trained in piano, explained in the same interview, classical music started out in 4/4 with the Baroque and Classical periods, but then later changed to 3/8, 6/8, 2/2, and all sorts of other odd time signatures as we crept into the modern period. She said, "Classical music was basically 4/4 and then it went into 4/3, too, which is just a waltz rhythm and all of that, but it just went further and further away from the heartbeat. Heartbeat is 4/4. Rhythm became very decorative, like Schoenberg, Webern. It is highly complicated and interesting—our minds are very much like that—but they lost the heartbeat." (Source)
Ragtime, with its syncopated beats, and impressionism, with its incredibly long measures, all broke the original 4/4 scheme; yet we still appreciated them for their beautiful abstraction. However, Yoko and Lennon felt that it was time again for music to return to the heartbeat, that simple, true 4/4 that follows the rhythm of our souls.