Business Origami is an empathy building activity during which end users create 'maps' of interactions between the various actors, objects, and locations they identify as components of a service or product.
Business Origami is Day 9 of 100 Days of UX, an exploratory effort to survey the 100 methods of design outlined in Martin and Hannington's Universal Methods of Design. For 100 consecutive days, I learn one new method a day and write about it.
The "Origami" in the method's name comes from the paper cutouts that are used to represent the components of the system. David Munoz's Business Origami article article for UXPA Magazine and Jess McMullin's primer on Business Origami are good sources for further reading on the topic. McMullin is of Citizen Experience, and they conduct design workshops with the method.