Shvirat hakeilim seems to be a Kabbalistic concept denoting how the light was created within the Genesis account. However, I cannot seem to find information regarding it. Can someone please explain to me what it is and back it up with sources.
Try this article at Chabad.org, which quotes (in translation) the classic sources on the subject.
Briefly, it's the idea that Hashem first created the ten sefiros as the "world of Tohu," as independent entities, where each one is is exclusively "thus and no other way" - i.e., chesed ("kindness") is pure chesed, gevurah ("severity") is pure gevurah, etc.; each one was so intense that it left no room for any of the others. This intensity caused them to "shatter" the "vessels" containing them, in much the same way that an intense light can damage one's eyes (which are the human "vessels" for the power of sight), or a loud noise the ear, etc.
The fragments of these spiritual "vessels," each of which was an expression of G-d's power and energy, are scattered throughout our world; these are the "sparks of holiness" often spoken of in Kabbalah and Chassidus, which it is our job to elevate by using for holy purposes the resources containing those "sparks."
Afterwards Hashem re-created the sefiros as the "world of Tikkun," in which each of them connects to and contains aspects of the others, much as atoms of different kinds combine to form the types of matter that we're familiar with.
The article cited above ends with this point: