What is the drain pipe in back of the house for (water leaking out of it)?

The pipe is either:

A) a vent line and the pipe is clogged and water is backing up through the vent line, but a vent line should be higher than the other drains in your house.

B) the normal drain for the shower and tub. I realize that this is probably not up to code but for some houses (particularly in old houses) they ran separate drain lines for things like the clothes washer and showers/tubs to reduce the amount of water going to a septic tank allowing for a smaller septic system.

He probably installed a clean-out access to make routing the system easier. If it is backed up to his clean-out you very likely have a clogged system. Give your plumber a call.