Leonard (Johnny Galecki) and Sheldon (Jim Parsons) are roommates and colleagues in the Caltech Physics Department. Together they have a combined IQ of 360, keep whiteboards in their living room in case a new scientific theory "just pops up" and, along with their friends Howard (Simon Helberg) and Rajesh (Kunal Nayyar), have a love for everything geek, from Sci-fi to World of Warcraft.
Leonard is an outcast among outcasts. He's proud of his intelligence and geek tendencies, yet he also desires to spread his wings socially, especially after Penny (Kaley Cuoco) moves into the apartment across the hall. Leonard immediately falls for her and sets out do to whatever he can to win her over. Penny's arrival sparks something in the lives of the other characters as well, introducing them to new experiences.
Many of the show's situations are built out of normal, everyday events, though viewed from a group of socially inept characters. At the same time, Penny is exposed to a world that is alien to her, putting her in the same spot as the guys.
One of the more common complaints I've heard is that the show tends to over exaggerate "geek culture". While a valid complaint, it is a silly one. Yes it goes overboard, but it doesn't do anything that other TV shows haven't done to other groups. It's no different than the stereotypes used in other shows only instead of "them" it is "us", so it's easy to see why some people might take it the wrong way. To be perfectly honest, I've either heard or participated in several of the conversations and situations in the show. While I've never gone so far as to play a game of Klingon Boggle (Boggle, but with Klingon words), I know people who would. Really, who hasn't found themselves in an ultimately pointless conversation about Superman's powers, the sportsmanship of Halo multiplayer matches or whether or not one of the members of the group was a robot?
The real reason for the show's success is the chemistry between the cast. Leonard and Sheldon are alike, yet completely different while Howard and Rajesh are the show's more outlandish personalities. Even the relationship between Penny and Leonard has a nice balance. There's enough give-and-take between the two that, at times, it seems like Leonard really does have a chance.
The Big Bang Theory comes with one extra, but it's a good one. "Quantum Mechanics of the Big Bang Theory" looks at how the show came about and features interviews with the cast and crew.
If the show has any flaws, it is that it sometimes goes a little too deep with its geek references. This might turn away a few viewers, but even if the references are obscure, the situations are relatable. Even if you aren't a geek, I highly recommend The Big Bang Theory.