The root system is the network of all the roots of a plant. It is the system of the roots and related organs that the plant develops.
The picture on top shows the many looks and types of the planting root system. The two main/basic types of root system types are:
1. TAPROOT system: this is a single primary root that dominates as the center in which branch roots develops around it growing laterally. This type of root grows vertically downward. Usually when a taproot system plant is pulled, the long taproot stays in the ground and re-sprouts.
2. FIBROUS root system: this is a network of fine roots with no central dominant root. These roots do not go as deep as the taproots, but they spread laterally growing from the stem.
More information about the two types could be found at: http://www.cactus-art.biz/note-book/Dictionary/Dictionary_R/dictionary_root_system_apparatus.htm
Link to photo: http://www.il.nrcs.usda.gov/technical/plants/npg/images/NPGp5_rootsys.gif