The term horizontal flow is used to describe the airflow of a given furnace or air handler. The term is only used to describe the airflow of the indoor system. In a horizontal flow furnace application, the air conditioner evaporator coil rest next to the furnace or air handler. In most applications, the furnace air filter will reside to one side of the furnace. In the application pictured, you can see the Honeywell Media filter next to the furnace on the left.
Many horizontal flow systems will reside in attics or crawl spaces that don’t have space for a traditional upflow or downflow system.