The light that was in our part of the universe when the Big Bang occurred is still with us....as it is with everywhere else. It's the CMB, or Cosmic Microwave Background, the photons that have had their wavelengths stretched out so far that the background temperature of the universe is now 2.6K (or thereabouts). What they are saying is that the light that is coming from objects that were separated from our little corner of the universe by a certain distance, is only now coming into our view. So two points separated by a distance "x" in the early universe, during the Big Bang, were out of sight of one another because the horizon distance of our part of the universe at that stage was close by. Now, 13.7 billion years later, the light which was travelling from those objects to us is now within the horizon distance between the two sections of the universe (due to the expansion of the universe) and has allowed us to see those objects. That is, the horizon distance has increased with the expansion over time. You have to remember that this distance of 13.7 billion light years is only to do with the light travel time since those objects began to shine light towards us. Their actual physical distances from the Earth are considerably greater, due to the expansion. An object that is, say 12 billion light years from Earth, in terms of that light travel time, is some 25-30 billion light years away in actual physical distance. That's why you see quoted figures for the actual size of the universe (well, at least our section of it), in terms of its radius, as being around 45-47 billion light years. Here's a site you can goto which will help you to understand what I have just written...
http://www.astro.ucla.edu/~wright/cosmolog.htm
and more specifically...
http://www.astro.ucla.edu/~wright/cosmology_faq.html
Hope that helps