Wikipedia
In digital electronics, the fan-out of a logic gate output is the number of gate inputs it can feed or connect to.
In most designs, logic gates are connected to form more complex circuits. While no logic gate input can be fed by more than one output, it is common for one output to be connected to several inputs. The technology used to implement logic gates usually allows a certain number of gate inputs to be wired directly together without additional interfacing circuitry. The maximum fan-out of an output measures its load-driving capability: it is the greatest number of inputs of gates of the same type to which the output can be safely connected.
In message-oriented middleware solutions, fan-out is a messaging pattern used to model an information exchange that implies the delivery (or spreading) of a message to one or multiple destinations possibly in parallel, and not halting the process that executes the messaging to wait for any response to that message.
Also fan-out in Software construction means the number of classes used by a certain class or the number of methods called by a certain method.