To go out into and endure bad or stormy weather. Usually used hyperbolically. Thank you for braving the elements to come pick me up.I know there's a slight drizzle, but if you can brave the elements, then you may go play outside for a while.
Go out in stormy weather, as in We've just about run out of food; I'll brave the elements and walk to the store. The use of elements for atmospheric agencies dates from the early 16th century but is rare today except in this expression, which is often used hyperbolically.