Lyrically, "I Feel Fine" is one of the most basic tunes the Beatles released, especially right after A Hard Day's Night. But for that simplicity, it was a powerhouse, same as "I Want to Hold Your Hand." Where the past year or so had proven they had nailed down a winning formula, and were learning to produce it at a higher rate (more songs on A Hard Day's Night sound like potential hits than on With The Beatles, for instance) they were taking extra care that the songs that were singles sounded particularly excellent.
Musically, this is one of the best things they did before Rubber Soul. As much as I love the arresting "clang!" that begins "A Hard Day's Night," the fuzzy, feedbacking "geeeooooonnnngggg" that begins this song might be the better touch. It hits just the right level of discord for rock and roll, then last just long enough for the listener to take it, sustaining until the song's main riff, that jittery, jumpy, excitable one that seems so much more involved and particular that the ones that came before. Maybe that's the point - Lennon wrote some of the most basic lyrics possible, with just the right harmonic hooks in the right places to make it sound so smooth, then laid it out over this very intricate, very particular riff, marrying complexity and simplicity into one two minute burst of awesomeness. The music says stuff the lyrics can't. It's exactly the kind of some you want to listen to over and over - just like a hit single should be.
In a way, that complex-simplicity dynamic is what I feel both love and music should be like... it should take a lot of work, but appear easy and natural.
The b-side was "She's a Woman," which actually sounds more like a cover than an original, aping late-50's R&B that the Beatles would have devoured in their youth. To modern years it kind of sounds like CCR, who were years away -- which kind of gives it a timelessness in addition to feeling like a very specific era.