Many little factoids about the song above, but anything really about the song? No.
So really what makes this such an amazing song, is it Paul McCartney's melancoly lyrics or the delivery, the quiet acoustic guitar and string qaurtet (which is actually the first time another musician besides the Beatles themselves played on a Beatles record). I would say it would be both parts combined as it usually is with great songs (surprise, that was a trick question).

Yesterday opens with a quiet acoustic guitar sound and shortly after McCartney's vocals, a few seconds later comes the hook with the string quartet. In about a minute all of the elements of the song have come together, and none leave untill the ending.
But a note about the ending, it really leaves everything unresolved, no happy ending, just a sad man left alone wanting to hide. John Lennon really didn't like this ending, his only problem with the song was that it ended without any resolvement, that didn't keep him from calling the song McCartney's first masterpiece, after the fact.

To tell the truth I have yet to hear a cover of any Beatles' song that comes anywhere close to the original, and even though many will continue to try to cover this song (and make it even more the most covered song ever) none will ever capture the emotion and melancoly of the original.