In a steam engine, such as a steam locomotive, exhaust steam, as the name implies, is steam after it leaves the cylinders. Most of the high pressure it had as live steam is gone; exhaust steam is generally at a pressure of less than a dozen pounds per square inch. However, there's still a lot that can be done with it.
The traditional use for exhaust steam is for draughting. The steam is ejected through the blastpipe (or exhaust nozzle), pointing up the dead center of the stack. This creates a partial vacuum in the smokebox, causing air and the hot combustion gases from the firebox to flow down the boiler tubes and boiler flues into the smokebox, and out the stack.
Exhaust steam can also be used in an exhaust steam injector to feed water to the boiler, and in a feedwater heater to raise the temperature of the water being fed to the boiler, making it more efficient.