I know what dogging is, but I didn't know where the term came from. The first time I heard the question, I had to go home and Google the answer. Its a term I throw around quite a bit, and I felt very silly not being able to give the history lesson.
The definition of dogging in door hardware is to mechanically retract a latch to allow a free swing. This is a common feature of panic hardware - the latch can be "dogged down" and the door can then freely swing. It is actually one of the main differences between panic rated hardware and fire rated hardware. Because fire rated hardware must have positive latching, it cannot be mechanically dogged open (some fire hardware can be electrically dogged open, which allows for positive latching should the fire alarm go off, but that's a blog post for a different time!).
Answering the question "what is dogging?" - that's simple for me! But to answer "why is it called dogging?" required more research.
According to Wikipedia, the source of all knowledge, "dogging" comes from the term "dog leg," which is a very literal way of describing a tool that is very allen wrench in looks - if you're familar with Ikea furniture, you know what an allen wrench is. A dog-leg can be used to open a variety of different gates, hatches, or mechanisms. Turning the name of the tool into the verb for the action is a pretty easy logical step.
So - "dogging" in door hardware was essentially borrowed from engineers and mechanics who gave a funny name to their tool.
And now you know!