This currency is used for trading on the in-game auction and at stalls. It can be obtained and spent in a number of different ways.
Like Gyth Notes, you can earn Gythil in the game for completing certain quests, dungeons, earning achievements, etc. Still, that currency is considered quite more valuable and you will not be able to earn as much of it as you might Gyth Notes.
Should you run short of Gyth Notes, the game will prompt you to pay the difference in Gythil. This is convenient when you have to repair your equipment as soon as possible, and have run out of the Gyth Notes. Also, Gythil can be used for contributions to the Guild Treasury. There is a daily contribution limit: 10,000 Gythil.
You can sell items to other players for Gythil by putting it up for auction or selling it at your own stall. Additionally, Gythil can be exchanged for Aurum at the current rate via the in-game store.