A reverse flush is where the maintenance guy will disconnect a fluid line for the transmission, usually at the radiator (or cooler), then attach a flush machine to fill the gap between the connections. They will then fill the machine with fresh transmission fluid and start pumping it through your transmission lines backwards of normal flow. This pushes fluid through the filter, cleaning it, and then transports the dirty fluid out to a waste catcher inside the flush machine. It keeps changing fluid until most all of the dirty (old) fluid is exchanged for new fluid, which won't happen if you use the "drop the pan" method. This method allows the change of fluid and a cleaned filter inside the transmission without the need to remove the transmission pan.
This method isn't necessarily dangerous for your transmission, especially for something like a first time flush. With older transmission, you'll find the transmission can have buildup which replaces the worn parts of soft parts (clutches, bands). When you do a reverse flush on these transmissions, there is the possibility this buildup will be removed. You wonder why this might be a bad thing? When you remove the buildup, all you have is worn bands/clutches left. Sometimes, after the flush, you'll find your transmission starts slipping and rebuild or replacement will be following not long after. The buildup will actually support the transmission and allow it to last longer than without it.
If you perform regular scheduled maintenance and the fluid is changed on time, this buildup will usually not occur. The reverse flush can usually be done without issue. It's in the older trannies which have not had the fluid changed where you'll usually see issues starting not long after a flush.