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Spline is used to denote either of two quite different design elements.
The flat spline or lath
A spline consists of a long strip of wood (a lath, not to be confused with lathe) fixed in position at a number of points. In older days shipwrights often used splines to mark the curve of a hull. The lath will take the shape which minimizes the energy required for bending it between the fixed points, and thus adopt the smoothest possible shape.
The origins of the spline in wood-working may show in the conjectured etymology which connects the word spline to the word splinter. Later craftsmen have made splines out of rubber, steel, and other elastomeric materials.
Spline devices help bend the wood for pianos, violins, violas, etc. The Wright brothers used one to shape the wings of their aircraft.
In 1946 mathematicians started studying the spline shape, and derived the piecewise polynomial formula known as the spline curve or function. This has led to the widespread use of such functions in computer-aided design, especially in the surface designs of vehicles.
The rotating spline or gearing mechanism
The word spline can also denote one of a series of ridges on a driveshaft which mesh with and equalize the rotation speed of a mating piece, thereby transferring torque. For instance, a gear mounted on a shaft might use a male spline on the shaft that matches the female spline on the gear. Manufacturers typically cut such splines with a broach.
"Spline (device)"