The Song (deserving of a capital S) is obviously known for being a love ballad, probably describing the hardship of a bump in the road. Nonetheless, my different take on it tries to be a bit more poetic. Paul, rather than writing of some girl that caught his fancy, wrote about the simpler days of youth. Don't get me wrong, he was already young at the time, but a musical artist tends to grow up fast--maybe prematurely, or worse, melodramatically. When we are young we don't even begin to think of our troubles, our mistakes last as long as our attention lets them, and more precisely there's just a lot less to worry about. Growing up, and accepting the path of this growth--realizing that there's no going back--that's what I feel Yesterday represents. Your mistakes don't just go away. The idea of "yesterday" is personified by the song... and why she had to go away is what troubles Paul most.
This concept, applied to love, rather than simply some girl, also fits perfectly. Young love is innocent and simple where a daisy is enough to convince a girl whether she loves him or loves him not. But once one grows, so does their idea of love. Love becomes life itself, engulfing a person's emotions (or at least does when there are hormones involved). Why this simple love had to go away with yesterday could have also troubled Paul... but I like the less mushy, "that's life" version more.
