The Netherlight Crucible lets you improve the relics on your Artifact weapon, and can be unlocked by all players with the Legion expansion pack. In order to get the Netherlight Crucible you will need to do the main quest line on Argus. If you're not able to get to Argus, check out this guide.
The quest chain itself should be pretty easy to follow, and starts in Krokuun, goes to Antoran Wastes, and eventually ends in Mac'Aree where you finish it. You need to complete all areas, and cannot skip directly to the Mac'Aree one, so prepare to spend a few hours doing quests. At one point you get the quest An Offering of Shadow, and upon completing this you unlock the Netherlight Crucible.
When patch 7.3 first arrived you had to wait until the beginning of week 3 after the patch to unlock the Netherlight Crucible due to the fact that each set of quests only became avilable one week after the previous one, but all quests are now permanently unlocked on all realms, so there's no need to worry about this anymore.