To climb is to go higher. When you ascend a mountain, you climb it, and when a song rises in popularity, it climbs the charts.
To climb something generally takes hard work, which is clear when you watch a toddler climb a jungle gym or a mountaineer climb a sheer rock wall. You can also climb things metaphorically, like when a soldier climbs the ranks from corporal to major. Prices can climb too, when they get higher, and you can climb a social ladder when you meet well-connected people at parties. The Germanic root is klimban, "go up by clinging."