Systems biology is the science that studies biological systems, which may be molecules, cells, organisms or even entire species, from a holistic perspective. Biological systems consist of a large number of components such as genes, proteins and metabolites. Apart from studying the function of those individual components systems biology focuses on the dynamic interaction in the networks of biological components.
Every biological system is in fact a hierarchically organised network of interactions. For example: Proteins interact with other proteins and make protein complexes. Several protein complexes can interact and make cellular organelles. Cellular organelles can interact and make a cell; cells can interact in a multicellular organ or organism. Systems biology attempts to map all those interactions.
More explanation of sytems biology can be found in this video from Virginia Commonwealth University: A New Frontier: Systems Biology