They consist of an outer annulus fibrosus, which surrounds the inner nucleus pulposus.
The nucleus pulposus is very fluid (like jelly), and acts like air in a pneumatic tyre. It can also shift slightly within the disc, depending on how the back is angled.
The annulus fibrosus consists of several layers of fibrocartilage, with the fibres of each layer running perpendicular its neighbours. (So it forms a criss-cross pattern). This is designed to be very strong.
As people age, the annulus fibrosus gets weaker, and the pulposus can herniate through it. This is called a slipped disc, and the nuclear pulposus may press against nerve roots, causing radicular pain.