The show centers around a small group of government agents tasked with investigating crimes utilizing strange and unexplainable scientific phenomena. The crimes are discovered to be a part of "The Pattern," a series of gruesome crimes that utilize cutting-edge scientific technology. Season One was concerned mostly with the development of the main characters as they face a new creature or technological criminal each week. In Season Two, it is discovered that there is an alternate universe closely linked to this one and that the cases the Fringe Division keeps coming across are related to forces from the other side.
The show follows FBI Agent Olivia Dunham, team leader. She is assisted by scientific genius Walter Bishop and his son Peter Bishop. Walter was a famous scientist until a catastrophe in his lab led to the death of one of his assistants and sent Dr Bishop to a mental institution for 15 years. Olivia tracked down Peter since he had sole authorization to release his father and is the only person who can take care of the elder Bishop.
The team investigates a new phenomenon each week; however, there are a few overarching protagonists. In Season One, the major antagonist is a scientist named David Robert Jones. Jones is a terrorist who makes a pretty fantastic escape (see if you can figure out how it was done) from a prison in Germany and starts conducting attacks in Boston. In Season Two, Fringe Division goes up against a villain from the other side called Thomas Newton.
Some major themes on "Fringe" are the dangers of the quest for knowledge, redemption and family. Walter Bishop is a brilliant scientist who has spent his career seeking scientific truth above everything. For this reason he uses methods that are considered unethical (experimenting on children and adults without consent and creating deadly creatures). Many of the cases Fringe Division investigates relate directly to his past research. His work with the division now is a form of redemption. Family is also a theme in "Fringe." When the show started, Water and Peter had not seen each other in over 15 years, but throughout the second season, their relationship improves markedly. In Season Two, you also see the team as a whole move from a loose collection of people who don't even get along well to a close-knit group that always backs each other up.
One of the aspects of the show that fans enjoy is keeping an eye out for the Observer. The Observer has appeared in every single episode of "Fringe." His job is to observe Pattern-related events but to not take part in them. He has, however, sometimes interceded in events and has even had a couple of conversations with Walter.