Certain recipes (for example, corn bread, buttermilk biscuits) caution against overmixing: you're supposed to add the wet ingredients to the dry with a minimum of agitation.
Why?
And, is this related to why my friend's recipe for cornbread states that "some lumpiness is preferred"?
In the type of recipe you reference, all of which are quick breads, the result is supposed to be tender, not chewy.
Wheat flour has proteins in it, which if agitated in the presence of water, will combine to form a new protein, gluten, which is very chewy. Sometimes, this is desirable as in yeast raised bread, where the gluten forms the structure of the bread, and gives it its bite and chewiness. In fact, this is why (most) yeast raised breads are kneaded.
Gluten development is not desirable in tender quick breads, like cornbread or banana bread. Biscuits are a type of quick bread where the lumps of butter will promote flakiness, but you still want a tender crumb.
The flour and the liquids are combined as quickly as possible, with the least reasonably possible agitation, to minimize the development of gluten, and thus maximize tenderness.
The idea of leaving some lumps is to help prevent over mixing, and thus toughening the product. Even if there are some small lumps of unmixed flour, the liquid from the batter will penetrate them in a few minutes during baking, and they will not be a factor in the final product.
