Pipes are a way of connecting two or more console programs so that the output of one becomes the input of the other. This allows simple programs to be connected together to do something complex. Visual pipes are a graphical equivalent. It can be very frustrating waiting for your computer to finish one task so you can start the next.
Each coloured box here is a separate program and task. They can be moved around just like the standard "Copying" dialog in windows for example. But unlike those dialogs these can easily be stacked by moving the dialog over another.
In the above example a Find program finds all the log files and passes their location onto to a shell script that scans the log files. Then there are moved to an oldLogs folder then zipped before the logs are destroyed. The important part is you don't need to babysit the computer or write and shell scripts.