Fine grained mineral component of soil. Lots of clay can cause a soil to be heavy and sticky.
Clay usually refers to mineral/rock grains in a soil that are very small (finer than mud and silt). Large proportions of clay will make a soil heavy, difficult to dig, and difficult for roots to grow in.
Clays are produced by natural erosion, deposited as river deposits (e.g. on a flood plain), ancient glacial deposits (i.e. boulder clay), or even from a soft bed rock (e.g. the Cretaceous clays of Texas and SE England).
In geology, clay has a second meaning and refers to a large class of sheet silicate minerals (kaolin is probably the best known example). These invariably form fine grained particles that are often clay sized - hence the duplicate meanings of the word: A lump of clay is probably made of clay sized particles of clay minerals!
This tag should be used for questions about clay soils. Typically these will concern soil improvement and the kinds of plants that can be grown in clay soils.