My thanks to Ed Barkmeyer of NIST for a classic Complex Event Processing use case, extracted from an exchange on the W3C Rule Interchange Format working group email list:

One can have a confluence of truly distinct technical events, all of which denote a single business event, and that is a CEP concern. 

My favorite example is the sequence of status reports from a manufacturing workstation:
1 - Process X step 7: in progress, machine state operating, workpiece state normal, heat sensor 3 in yellow zone
2 - Process X step 7: control error, machine state recovering, workpiece state normal, heat sensor 3 in red zone, heat sensor 4 in yellow zone
3 - Process X step 7: unrecoverable error, machine state going safe, workpiece state unknown, heat sensor 3 no data, heat sensor 4 in red zone
4 - Process X aborting: at step 7, machine state safe, workpiece state unknown, heat sensors 3 and 4 no data, operator intervention required.

The business event can be summarized as: “there is a fire in the workstation”.