Seriously, if it's just an ingredient in something larger, is it going to make a difference if the butter's been clarified or not?
You can heat clarified butter to a higher temperature for two reasons -- you remove the milk solids, which can burn, and you remove the water, which will boil at 100°C and cause spattering.
In baking, clarified butter's lack of water means that it can't develop gluten as you would with simple melted butter. It's actually more similar to other oils than it is to melted butter when baking.
In the case of ghee, my understanding is that because it's from a warm country, part of the reason for making it was as a preservative, as the ghee would have a longer shelf-life (months) than standard butter in the local climate.
Raising the smoke point is the first reason. The second is that you remove most of the milk solids when clarifying, so people who are lactose intolerant can usually eat clarified butter. And third, clarified butter can be kept at room temperature without spoiling. I keep mine in a french butter keeper on the counter for up to a week.
The main purpose that I am aware of is to raise the smoke point while retaining the buttery flavor.
A sauce made with clarified butter may have a more subtle and, some say, refined taste