Answer:
A fibrous root system is a shallow, network of numerous roots and are a predominate feature of monocotyledonous plants (although a number of dicots also exhibit them). Fibrous roots are also a prevalent feature of shall, annual, herbaceous and desert plants. As these plants are relatively small a fibrous root system is sufficient to anchor them to the ground.
Fibrous systems are shallow and are intended to collect the largest amount of surface water possible.
The opposite of a fibrous root system is a tap-root system where several strong downward anchor roots are formed, these are normally associated with large plants such as trees and shrubs.