Any material that is heterogeneously made up out more than one base component. This rules out alloys, which are smooth mixes of different metals, but includes materials such as fiberglass, plywood, particle board, etc.

The vast majority of composite materials are made by combining thin fibers with high tensile strength with something goopy. Fiberglass is a combination of glass and resin, particle board is a combination of wood fragments and glue, etc. Materials produced in this was are ideally strong from the fibers, but flexible from the goop. Another advantage is that the materials are much lighter than comparable solid materials that have the same tensile properties.

Plywood is a different type of composite material, in that it is created by laminateing thin sheets of wood together in such a way that in each sheet, the grain runs a different way. This decreases the likelihood of the board to split, since there will always be a grain running in the pertainent direction.

Composite materials were designed the same way as most great engineering innovations: by blatantly ripping off Mother Nature. Wood, bone, and muscle are all good examples of natural 'fiber + goop' composites, and skin is a good example of the laminate approach.