Once you have met Jun Ortoi, you will begin encountering the Immortal Syndicate. If you manage to defeat an Immortal Syndicate member, they may drop a Veiled Item. Veiled Items are special rare items with Veiled Modifiers - modifiers masked by ancient magic that only Jun Ortoi can reveal. When Jun unveils the modifier, you'll be presented with three different options for what that modifier will ultimately be. Not only are many of these modifiers very powerful, but unveiling them allows you to craft those modifiers using your Crafting Bench in your Hideout! So your choice is very important, even if you have no plans to use the item it appears on.
Veiled modifiers often have multiple tiers, which can only be learned for crafting by unveiling the same modifier several times, and some can only appear on items from specific Immortal Syndicate members. You can check whether a Veiled modifier is from a certain member before you unveil it by looking at the advanced modifier description (enabled in Settings). Once you have unlocked a Veiled modifier for crafting, it will be available for all of the characters you create in that league. Veiled modifiers are considered crafted mods, even if you didn't craft them. That means that, under ordinary circumstances, you won't be able to craft additional modifiers onto an item you have unveiled. One final thing to consider: even if you have unlocked all the Veiled modifiers you want, Veiled items still have value -- to other players! Some players may pay a premium for items that have not yet been unveiled, so that they can rapidly learn the recipes! Consider selling Veiled items to other players!