When you finish a synthesis, based on your quality you have a chance of HQing (High Quality) the result.
What touch up does is basically say, "Hey, I have extra durability, and I didn't get a HQ". What you can do is sacrifice some of that durability in order to reroll for a HQ. Sometimes you get it, sometimes you don't, it's completely random.
Touch up takes anywhere from 7 durability to 20 (20 if it's sparking), so be careful. You can still botch it using touch up.