There are two interpretations of 'Mountaineering' depending on the context in which you use the word:
Mountaineering is any activity in a mountainous environment. It includes rock climbing, ice climbing, hiking, orienteering, skiing, and 'mountaineering' in its own right (see below)...
Mountaineering as a specific activity is usually used to include climbing of a whole mountain, encompassing a wider variety of skills than simply rock climbing. For example, climbing up a cliff face might be rock climbing, but climbing Everest is mountaineering as it requires ascending a complete mountain, and uses skills from rock climbing, ice climbing, survival, navigation, endurance etc.
But there is a grey area in this. Is climbing El Capitan in Yosemite rock climbing or mountaineering? What about if you climb an unclimbed face of a mountain in the Himalaya, but without trying to summit the mountain? At the end of the day, it boils down to the seriousness of the adventure.