A League Of Our Own
(If you are playing on the permanent Standard League, you can skip this page.)
If you've followed my recommendation, your character has been created in the current league - as of this writing, Legion (which started in early June 2019 and should last until September 2019 or so).
This page is about the mechanics of the Legion League, and will update with the release of future leagues. Previous league information can be found in the Mechanics Reference under Past Leagues.
An Eternal Conflict...
As you venture through Wraeclast, you'll occasionally encounter Timeless Monoliths.
Interacting with one of these Monoliths begins an encounter with forgotten, time-lost armies of the past. The encounter comes in two phases. First, you have a limited time to free as many frozen monsters as possible by 'killing' them. And second, you have to actually fight the monsters you freed.
In addition to the rank and file, there will be chests (which still have to be attacked and 'freed' but not fought afterward) and special monsters marked with symbols. Defeating these will yield specific kinds of loot, depending on the symbol displayed.
This monster's symbol indicates it will drop an Essence item when defeated...
...while this chest holds a Unique item.
In general, the best rewards are found at the far edges of the two warring armies (in other words, from the monolith, you'll want to head directly into one of the two armies in a direction perpendicular to the lines of enemies). You'll often find a special boss (a "General") or a very large chest there with lots of Timeless Splinters (see below for more on these).
The Legion league introduces a new sort of indirect item drop called an Incubator. Incubators are consumable currency items that you can apply to equipment, causing an item to drop after some very large number of kills with that item equipped.
When an incubator is close to being filled up, it'll show up on the right side of your screen, the same way a gem close to leveling would. Once it's full, its associated item just shows up like any other drop. Once the drop appears, the Incubator effect vanishes from the equipment it's attached to, so Incubators only get you one drop of their associated item. Think of them as just "more loot, but delayed".
In general, Incubators appear to be safe to use while leveling (in the sense that you won't miss out on some exceptional drop), with the caveat that you should use them on an item you expect to keep equipped for a while (otherwise you might want to replace it before the special drop is finished incubating).
Splinters, Emblems, and Timeless Conflict
There are five armies locked in the timeless conflict, each of which appears to have an associated color: Eternals (white), Karui (orange), Maraketh (yellow), Templar (green), and Vaal (red). Each is a major faction from Wraeclast's history.
Defeating enemies and looting chests associated with a particular army can drop Timeless Splinters associated with that army. Collecting 100 of these combines them into a Timeless Emblem. Emblems can, in turn, be inserted into the endgame Map Device to open portals to the Domain of Timeless Conflict, where the armies you've encountered are locked in eternal battle. You may even find the Generals of these armies there.
(If past leagues are any indication, expect these Generals to be endgame bosses of middling difficulty with specific Unique drops. But I can't confirm this as of this writing.)