To broaden something is to make it wider or more expansive. If you wake up feeling less than cheerful, the sight of the doughnuts your dad got for breakfast might broaden your smile.
Something can broaden literally, like a river that broadens as you hike beside it, growing wider as it flows south. Things also broaden figuratively, the way people's minds tend to broaden when they travel around the world and meet people from different cultures. In both cases, things that broaden expand and become more open.