Designed for scrambling up steep and exposed rock while being able to travel long distances, an approach shoe is a cross between a hiking boot and a rock climbing shoe. Most often used in mountaineering sports, the shoes are given their name because they reference the approaching path the wearer must take to get to a rock climbing destination. Depending on the area, the approach can be a mixture of walking, hiking, and scrambling up rocks. 
Because there is often steep and exposed terrain (meaning there is a drop-off on one side of the path) encountered in rock climbing approaches, the shoes are more than just a hiking boot with a sticky rubber sole. The laces of an approach shoe usually extend down the entire area of the foot — like a climbing shoe — to ensure a snug fit that is helpful for getting up rocky terrain.
Approach shoes have a specialized sticky rubber sole that can adhere to rocks on a steeper gradient than a hiking boot would. The outer area of the shoe that surrounds the toe area — called the toe rand — is also made with this same sticky rubber for extra protection against scuffing and to perform well in situations where climbing is necessary.
Compared to a hiking boot, the sole of an approach shoe is made from softer rubber to ensure flexibility for scrambling up rocks. If you compare the sole of a hiking boot to an approach shoe, you'll notice that a hiking boot usually has deeper set lugs to ensure greater traction on dirt and ground. The flat, smoother surface of an approach shoe adheres better to rock than the lug soles of a hiking boot does — especially on slab terrain, which is vertical, flat rock lacking natural places to grip.
