At base level 160 a new instance will unlock called Palace of Ghost. This instance drops memories to use for the equipment memory system. Once you have received your first drops you can access this system.
Open your inventory and at the top where all the filters are cliick the bottle icon on the far right. To access the interface click on any memory and choose Memory Upgrade.
There are three qualities of memory: green, blue, and purple. Their quality determines their level cap:
Green, max level 10
Blue, max level 20
Purple, max level 30
Each upgrade increases your Max HP, Atk, MAtk, Def, and M.Def. Every ten levels also unlocks a passive bonus which rolls randomly from a preset pool for each of the three lines. While the flat bonuses are nice it's these passives that you truly care about.
While these passives are random you can actually change them to whatever you want rather than having to continuously re-roll them. This is expensive for the third line so chances are you'll keep maxing these out until you get your preferred third line then re-roll the first two passives if you need to.
Example of fully upgraded Memory
Open your bag and select the Memory tab filter on the top right of your bag, then select the memory to equip and choose "Load Memory". This brings up the Add Memory interface to choose where to equip this memory. You can equip them to your Weapon, Armor, Cloak, Boots, and Accessory Slots for a total of six equipped memories.
Equipping a Memory
Example of Add Memory screen from previous patch
When you first open the Memory Upgrade interface you'll be shown the selected memory and what it takes for the next level. You can change this accessory out by clicking on the icon for it above the level up selector, then selecting a different one to upgrade.
You have to do this to work on existing memories as I have not found a way to see your currently equipped memories to work on them.
In the example to the right my next upgrade for this level 1 purple quality memory costs 5 Memory Afterglow. These Memory Afterglows are the resource needed to upgrade all memories regardless of quality. You'll receive some from your weekly Equipment Memory dungeons (such as Palace of Ghost) but you can also get more by dismantling unwanted memories.
Memory Upgrade interface
Breaking down unwanted memories creates more Memory Afterglows to use in upgrading memories. To access this first open your memory upgrade interface, then select the bottom tab on the right side to open the dismantle interface.
Select the memories you want to get rid of and click Decompose to break them down into Memory Afterglows and Memory Crystal Cores.
Amounts obtained are as follows:
Green = 1 Memory Afterglow
Blue = 5 Memory Afterglows
Purple = 1 Memory Afterglow and 1 Memory Crystal Core
Additionally, there is an option to automatically dismantle accessories of green and blue qualities. Since you should never be upgrading these two you should probably turn this on.
To do this, click on the blue gear icon to the right of the decompose button and check the box for both green and blue quality, then save settings.
Accessing Dismantle Memories and Auto Dismantle Settings (gear icon)
Auto Dismantle Dialog
To change passives open the Memory Upgrade interface, then select the center tab on the right side to open the Select Memory Words interface.
Here you can select any of the three lines and change them to a passive of your choice. This costs Memory Afterglow Crystals and gets more expensive as you select passives that require a higher level to unlock. This makes the bottom passive the most expensive to replace.
The cost to replace as are follows:
1st Line: 1 Memory Afterglow
2nd Line: 5 Memory Afterglows
3rd Line: 100 Memory Afterglows
Since the third line is so expensive you will probably upgrade a few purple quality memories to 30 before you have enough to do this for just one third line. You should probably upgrade several purples before choosing to do this since you will save a ton of afterglows in the long run if you happen to roll what you need.
There are quite a few passives and you can see the list and change them by selecting one of the three lines on the right side, then clicking Select Words to bring up a list on the left to choose from. You'll notice that each of the three lines pulls from a different pool.
Memory Word Selection
List of words to choose from for the third line