In the world of music, and specifically synthesizers, a patch is historically known as a configuration of equipment created by interconnecting them with “patch cords” (and possibly also patch bays). The action of making these connections is known as “patching.” Back in the old modular synthesis days, sounds were created through the patching together of various components or modules of a synth and then refined through adjustments made to the controls of each section. In modern synthesizers the different configurations and algorithms are generally stored as a set of parameters in memory, but are sometimes still referred to as patches just the same.
In the software world a patch is a quick modification of a program, which is sometimes a temporary fix until a particular problem can be solved more thoroughly.