What is the relevance of the stat ATK?

To a priest, there really is no relevance. :)

Actually it affects how often you hit the target I believe and +ATK is a really big deal to melee. It makes little difference to us though.

EDIT: That isn't completely true. I <em>do</em> notice I miss a lot less often when I have melee type ATK buffs. I just meant that unless you melee a lot (and priests don't usually) that it isn't important to worry about for you.

ATK is a composite figure combining both your ability to hit a target with a weapon and the amount of your hit.

More ATK = you're a bigger, badder melee.