Haha HQ= High Quality.

Every bit of crafted gear can be high quality, with the right moves.

The game does a good job of teaching you what's what. You'll get it more once you actually start crafting. As a note, you can't HQ any gear until you have a level 5 DoH (doesnt take long at all). You get your first "Touch" ability at level 5, and it's these touches that increase quality.