I think they are random, crystalized pieces of LOVE.
I think the same thing for the little hearts you get out of bushes and stuff. (Ever since I read someone on TV Tropes conveying the idea).
I have some theories about Hyrule in regards to the magical essenses in the land: I think that the general magic inherent in that universe causes things to become manifest in our world that remain invisible in ours - such as emotions and "spiritual" types of things. I remember the Poe Salesman of Ocarina of Time talking about how the Poes are "pure hatred" that's manifested itself into Poe-form, indicating, (with a few exceptions) that the Poes aren't really ghosts of the dead so much as just manifested despair and anger. Link also has to fight Dark Link in that game, which I think is a manifestation of his "sins" and "inner darkness" - his potential to be evil. Unlike all of us, who must battle our demons from within, in Hyrule, they get, at least in part, the magic of the land turning those inner demons into outer ones - which can be taken on with a sword.
And I think that good emotions, love is the same way... much like Skyward Sword's Gratituded Crystals were people's thankfulness given form, I think random feelings of love and caring find their way into the ether and crystalize in random places as heart pieces.
And sometimes, boss monsters hide this love and try to devour/ destroy it, which is why there is a bit of "crystalized love" within each of them after Link destroys them.
Or it could be just a handy game mechanic... the first game, Shigsy decided that hearts made a cute life-meter and just rolled with it when it became popular (or maybe after players got annoyed at the boring "life bar" of Zelda II ).