Disclaimer: This is a simplified view to give you a general idea, its not the beginning or end of what you can do with mule (or other service buses)
Mule is a message processing engine. You can think of it as a giant conveyer belt. You put something on one end, and it goes along the belt and comes out the other end.
The thing that mule deals with are called messages.
The starting point is the "inbound end point" and the exit point is the "outbound end point"; between these pairs of end points you can have other things that will process the message as it travels from the start to the end.
A combination of a start end point + gubbins in the middle to do some work on the message + outbound end point is called a flow. You can chain flows together to create a workflow or process.
These processes are then packaged as an application and uploaded to the mule server. The process only runs when a message that it is listening for arrives. Otherwise the processes are sitting idle. Think of it like a car assembly line. The assembly line that fixes the seats in the car can only start when the chassis is finished; otherwise there is nothing for it to do. Once the seats are fixed, only then can the paint assembly line start, and so on.