From my layman's perspective after having watched probably every space documentary produced for channels like the Space channel and Discovery's conglomeration, the big bang happened and propelled matter out from the source but now, billions of years later, space is expanding not only from this source but also between everything that was propelled from this initial blast.

If you likened that to the USA, the big bang happened in central Iowa, but things aren't just expanding from the source in Iowa, cities like LA and San Fran are also expanding away from each other at an accellerated rate. AFAIK, the leading theory is that dark matter is causing the intra-galaxy expansion, but little is known about dark matter and what drives this expansion. This is why it is believed that the universe will die a cold death (where all solar energy burns out) rather than collapsing in on itself since everything is moving away from everything else. At a certain point of expansion, nothing will have a gravitational effect on anything else.