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I found the following explanation of the Frisco 1522 website ... as clear as any:
"What is a feedwater heater and does 1522 have one?"
"In the normal course of operation, a lot of heat energy goes up and out of the smoke stack (steam engines are not very efficient). If some of this heat could be transferred to the water being added to the boiler, it would reduce the amount of fuel needed to bring this additional water to boil. Feedwater heaters take the steam exhausting out of the cylinders and transfer some of this heat to the water going to the boiler, or feedwater, to raise its temperature."
Hope that helped.
John
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The City of Saint Louis (UP, 1967) is still my standard for passenger operations