Beyond the obvious fact that the show and its characters are science-themed, I would suggest that some insight can be found through the lyrics of the theme song by The Barenaked Ladies:
Our whole universe was in a hot dense state,
Then nearly fourteen billion years ago expansion started.
wait...
The earth began to cool, the autotrophs began to drool,
Neanderthals developed tools, We built a wall (we built the pyramids).
Math, science, history, unraveling the mysteries,
That all started with the big bang! Hey!
The Big Bang theory (leavingthe theory itself, not the show, and leaving aside actual discussions of inflationary cosmology) is about unraveling the origin and development of the universe. The Big Bang also represents the beginning of the chain of events that lead to the development of humanity.
We developed tool use and changed the landscape around us by building things. We developed math and science as disciplines to help us understand our reality, and the study of history brings that understanding a step closer to us by focusing on our own development and impact on our species.
As we unravel these more prosaic mysteries, so too do we unravel the mysteries of the human condition. Comedy and drama have long been ways we as a species express thoughts and concepts about our humanity. The show addresses many of these themes, such as: honesty and communication, love and friendship, communication,cooperation and competition, love, friendshipfear and confidence, etc. In its own small way it contributes to the understanding of the mysteries of being human, which all started with the Big Bang.