"Systems biology" represents a significant shift both in the way biologists think about their field and in how they go about investigating it.
A central tenet of most scientific endeavour is the notion of reductionism—the idea that things can best be understood by reducing them to their smallest components. This turns out to be immensely useful in physics and chemistry, because the smallest components coming from a particle accelerator or a test tube behave individually in predictable ways.
In biology, though, the idea has its limits.
A complete understanding of biological processes means putting the bits back together again -- and that is what systems biologists are trying to do, by using the results of a zillion analytical experiments to build software models that behave like parts of living organisms.
Ultimately, the aim is to build an entire virtual human for researchers to play with.