Since Skyward Sword was released, theories have emerged speculating that the Light Force is the power of Hylia left within Princess Zelda's bloodline. However, those theories generally disregard The Minish being the ones to deliver it along with the Picori Blade, as told in The Minish Cap's intro.
It is most likely not a fourth piece of the Triforce. Beyond the 'Tri' meaning 'Three', each individual piece is associated with a Golden Goddess. For there to be a fourth Triforce piece, surely we would need a fourth Golden Goddess too. If that were the case I'm sure it would have been at the very least mentioned at one point. The fact that it hasn't makes me think it is not likely.
We can see how The Minish have access to quite powerful magic by way of Ezlo creating a cap which grants wishes (Vaati is proof that the magic in that cap is quite powerful indeed) so it may just be that the Light Force is some form of that magic given to the Hylians to fight off the evil that filled the world at that time.
That's just pure speculation mind, we don't have nearly enough information for a definitive answer.