Perseverance is not giving up. It is persistence and tenacity, the effort required to do something and keep doing it till the end, even if it's hard.
Perseverance originally comes from the Latin perseverantia and means to abide by something strictly. This makes sense, because if you're doing something in spite of all the difficulty, you're being strict on yourself. Sailing around the world and climbing Mt. Everest are acts requiring perseverance. Even things like learning a new language require perseverance and daily practice.