This is an electric coolant pump, controlled by the climate control system, that will pump hot coolant through the heater core inside the car. It is intended to provide better heating for the passenger compartment, especially when the engine is idling (at which time the car's mechanical water pump isn't turning very quickly).
My auxiliary coolant pump was leaking a few weeks ago too, just as you described. A new pump was quoted at $130 to $180 (parts only) depending on where you buy it.
I replaced it with a copper PEX elbow pipe fitting (available at Home Depot for around $1). It fits perfectly, and has nice ribbed ends to make sure it stays in place. I didn't even have to drain the coolant from the car to replace it - just clamp off the hoses on either side of the pump with vise grips to stop major coolant loss, and then quickly pop out the pump and replace it with the elbow pipe fitting. I only lost about 3 cups of coolant in the process.
So far, I have noticed NO DIFFERENCE in the climate control system operation - the car heats up just as fast as before (and it's been cold here, -20°F), and the hot air is just as hot as always. So, no more leaking coolant, no loss of performance, and a lot of money saved...
I intended for this to be an interim fix until I could find a more economical replacement pump, but given that there's no loss in performance whatsoever, I think I'll keep it as-is.
If you're on a budget, note that this type of pump is used on a lot of other german cars (VW, BMW), so if you're desperate for a replacement pump, you could find a similar non-Mercedes replacement at an auto wrecker and just solder the MB connector onto the 'new' part so that it fits in your car.
