Fan-in generally refers to the process where multiple producers produce data and pass it into a single service or message router. The term is most commonly used in digital electronics to denote the number of inputs that a logic gate can handle. For example, an AND gate with four inputs has a fan-in of 4.

Fan-out generally refers to the process where a service or message router delivers messages to multiple consumers, mostly in parallel. In digital electronics, the fan-out of a logic gate output is equal to the number of gate inputs it can drive. For example, one output may be connected to several inputs. 

Fan-in and fan-out patterns can be used together with distributed messaging applications to decouple producers and consumers. A fan-in process decouples producers from the service, and a fan-out process decouples the service from the consumer. The fan-in and fan-out patterns may be used with producers and consumers of the same type (if their throughput requirements differ) or with producers and consumers of different types.