The refine system allows you to get increased stats for your gear AND a new line on top of that. Some notes about this:
Stones are scarce so please don’t refine pieces of gear that have bad stats, focus on your best pieces first and save the rest.
Blue stones: You can obtain them with the exchange shop and some game modes like the Party raids. You can also craft a few every week.
Yellow stones: These are paid only (for now) as far as we can see currently in the Korean version. Some events give us one or two stones.
Like everything in this game; ATK%. Focus on your weapons first.
Priority really depends on the character after that. Your damage dealers will benefit from Crit damage and HP always helps with the combat power deficits.
For units like Erin, you want to prioritize the trinket since HP is perfect for her shields.