This is an interesting question, because it relates to Chinese language. I know Amy is Korean, but I cannot help but put it in the Chinese context. Many Chinese people, when asked about their hobbies, list "mountain-climbing"（爬山）. (The first time someone visits the Great Wall, it is traditional to climb the stairs 爬山.) I was a little taken aback when I first ran into this, because mountain-climbing (mountaineering), as Karissa says, requires a lot of equipment. Mount Everest（珠穆朗玛峰）attracts mountain climbers. So 爬山 is better translated as hiking, although that still doesn't quite capture the idea. A hike is a walk, usually a long walk, from one place to a planned destination. "Climb" is a general verb meaning to ascend.

Climbing can be many things, from climbing a ladder, to stairs, to even a mountain. Climbing is the basic verb describing the motion of moving up something. Mountaineering means only climbing mountains, this implies use of a lot of equipment and preparation. Hiking means going for a walk in a natural environment-so not just outside, but in an area away from houses or buildings. It can be really easy, or really hard, depending on how hard the hike is, and how far you are going.