Skills
From Toadwater Guide
When you perform an action related to a skill in Toadwater, your dwarf gains skill XP (and overall XP which determines your level, not to be confused with worth). If your action succeeds, you dwarf generally earns more XP than when an action does not succeed.
When your dwarf gains enough XP his level in that skill increases -- each level takes more XP than the last. Your dwarf also gains skill over time -- see age for more info.
The higher the skill, the better the odds of of success. ToadStat is an excellent tool for calculating odds of a given action.