A double-wing formation is a combination of a basic enclosure with extensions along the two adjacent sides. A double-wing formation is a good thing to have: it is not difficult to understand that in such a position, your stones are working together effectively.
In this example, Black has a double-wing formation based on a small low enclosure in the upper left corner. Doesn't it look a bit like a bird stretching its wings along the top and the left side?
--Stefan