A common need is the graphical showing of hierarchies, containment, origination or classification, which can be represented as one-to-many relationships in a Tree structure. Tree in the sense of a root with many branches, usually shown downward for reading purposes. Examples of these are organizational charts, containment diagrams or navigational controls in software applications. A special application of trees is the representation of space or usage as areas such these shown in Treemaps. A very good explanation of trees and treemaps can be found here.
Also there is the radial representation and navigation in the so called Hyperbolic Trees, either in 2D or 3D views.
The problem with this structure is that each node can have just one parent or dominant, making it not always suitable for reflecting reality albeit simple to understand and affordable for implementation.