A cleave in an optical fiber is a deliberate, controlled break, intended to create a perfectly flat endface, perpendicular to the longitudinal axis of the fiber.

A cleave is made by first introducing a microscopic fracture ("nick") into the fiber with a special tool, called a cleaving tool, which has a sharp blade of hard material, such as diamond, sapphire, or tungsten carbide. If proper tension is applied to the fiber as the nick is made, or immediately afterward (this may be done by the cleaving tool in some designs, or manually in other designs), the fracture will propagate in a controlled fashion, creating the desired endface.

A good cleave is required for a successful splice of an optical fiber, whether by fusion or mechanical means. Also, some types of fiber-optic connectors do not employ abrasives and polishers. Instead, they use some type of cleaving technique to trim the fiber to its proper length, and produce a smooth, flat perpendicular endface.

Source: from Federal Standard 1037C