Below is a walkthrough for the Raise Magic Skills task in Rune Factory 5.
Client: Cecil
Objective: Raise one of your magic skills to 15
Reward(s): Water Laser x1
After accepting the task from the Task Board, Cecil will task you with leveling up one of your magic skills to level 15. You can do this by either using one of your rune spells or equipping a rod and defeating enemies to level up the skill. Once one gets to 15, return to the Task Board to complete the task.