When you made something broader or more open, you widen it. In order to add bike lanes on your street, the city may need to widen it.
Your friend's smile will undoubtedly widen when you hand him a chocolate cupcake — in other words, what starts as a grin gets bigger and wider. A scholar who widens her area of expertise adds subjects to her research, and your dinner options widen when two great new restaurants open in your town.