The Augment system allows you to tackle specific content for a chance at Psyche items, which will allow you to further increase the stats of accessories. Each dungeon has its own unique Psyche related to the augment system, in addition to Dragon Trader Junsorei selling certain Psyches. Battlefield Traders have their own PvP-focused versions.
After receiving the required material for the Stats that you would like to increase, Shift + Left click on the item in your Inventory that you wish to apply an augment to and it will open your Manage Equipment window. There you’ll see the Augment tab. The cost to augment your gear each time is two Transformation Stones and 15 gold, but you can only augment an item a maximum of six times, keeping in mind that it may not take that many times to get the maximum amount. If you change your mind and want to use a different Psyche, you can, but just be aware that augmenting with a different Psyche will start you from the beginning once again.