A walking stick not only helps balance you, but can extend your daily walking range by allowing you to momentarily transfer some of your weight (you and your backpack) from your legs to your arms and down the stick. It's kind of like having another leg to walk with.
Using a walking stick regularly can also help to build muscle in your arm, especially for people who are out of shape. If you use a stick, don't forget to learn how to use it with both hands -- not as easy as it sounds. Holding it in your dominant hand will come easy. Don't try to force the strike of the stick with your footfalls. Your body will find a rhythm that works for you. Start to notice how your arm feels. Walk with the stick and then without. Notice how much lighter your feet feel when using the hiking or walking stick. Soon, you too may become a fan.
Walking or hiking sticks are best adjusted to the user's height. I'm about 65 inches tall and like a stick that's about shoulder height. My hand rests on the top of the hand grip, about 4 inches below the top of the stick, which allows me a comfortable swing of arm and stick as I walk. There may be a better formula, but that works for me.
Walking sticks have other uses, such as prodding wildlife from your path or breaking pinatas, but other bloggers have more expertise in those side benefits. I just know that I move a bit faster and can go a little farther using a hiking stick than going without one.