The benefits of walking on hills can be explained by basic physics. When you heft your body up over hills you are going to expend more energy than when you are just walking on flat ground. Depending on what slope you are walking at, walking up a hill can actually burn between two and four times as many calories as walking on ordinary flat ground. Walking on a hill can also tone your calves, your butt and other core muscles in your body.
The ideal hill for walking is one that is steep enough that you are boosting your effort level without it actually leaving you at a point where you cannot keep walking. If you happen to live in the hill country, then you may have this type of terrain in your very own neighborhood. If you do not have hills nearby, then consider looking for local wildlife areas and state parks. You might also be able to do this on shallow stairs, such as the stairs leading to a public building for example.
The slope of the hill is going to dictate how much of it you actually integrate into the workout that you are doing. You should be warming up on a surface that is flat, and then begin your ascent up the hill. On a long gradual hill you should be aiming for a steadier pace. For shorter and steeper hills you should be aiming for pushing yourself up and over to the top so that you can reward yourself by catching your breath on the way back down.
Walking down hill can also increase your calorie burn as well. Descending a steeper include is going to work the muscles in your leg and your torso more than usual because your downward momentum has to be controlled to keep your body working upright.