A fibrous root system (sometimes also called adventitious root system) is the opposite of a taproot system. It is usually formed by thin, moderately branching roots growing from the stem.
Most trees begin life with a taproot, but after one to a few years change to a wide-spreading fibrous root system with mainly horizontal surface roots and only a few vertical, deep anchoring roots. A typical mature tree 30-50 m tall has a root system that extends horizontally in all directions as far as the tree is tall or more, but well over 95% of the roots are in the top 50 cm depth of soil.
Weeds that have fibrous root systems can be hard to pull from the ground. Pulled weeds may grow back from any roots that were left in the soil.
Definition adapted from URL: http://en.wikipedia.org/wiki/Fibrous_root_system