You can use a 6* copy of the same character as material to increase one of the original’s skill level. Enhancing the skill permanently boosts its damage, effect, duration, etc. You can use a lower-grade copy of the character; however, the enhance rate will be significantly lower. A 6* copy is strongly recommended since it has a really high success rate. Skills of SR and R characters will be easier to enhance since duplicates are easier to get compared to SSR characters.
The skill you have to boost will depend heavily on the character’s intended utility. For example, for the SR water support character, Lydia, it’s worth focusing on enhancing her Skill #2 (Prophecy of Salvation). At max level, this skill can revive 1 ally with 100% HP and DEF +40% for 3 turns. For attack characters, enhancing their most powerful attack (usually Skill #3) should be prioritized.