Covenants are sort of like the Legion Order Halls, in that they are combinations of building and story arcs. As you advance with them (measured by renown), additional bits of story will unlock, and so far these have been interesting/different in each of the covenants. The minimap has an icon for your covenant, click on that to see what renown you have and what’s available to do.
Covenants are also the source of soulbinds. These are talent trees, with more talent choices opening up as you increase the renown with your covenant. They are different from the classic talent trees, in that your choices are determined by drops (items you get in the world) called conduits. These conduits are little bits in your bag that you take back to the Soulbind table in your Covenant (“Forge of Souls”), right click on them and they are added to the list (you don’t carry them in your bag any more). There are 3 kinds of conduit—endurance, finesse, and potency. Each of them provides different a kind of bonus to your character. Early on, you won’t have many conduits to choose from—just select the best of what you’ve got. It doesn’t cost gold or anima to change conduits; there are some glowing lights at the bottom of the screen and it uses up one light to change each conduit. The lights restore each day, so it’s cheap to make mistakes, er, try out different things. Don’t overlook the usefulness of the soulbind talents that give you bags of crafting materials when you kill things. )
Each covenant has a sanctum that you can build up. Every sanctum has 4 buildings: a transport network, an “anima conductor”, an adventure table, and a special building. The NPC that lets you build the buildings and upgrades them is also the one that will collect the anima tokens from your bag and put them in your reserve. The Adventure Table is the first thing you’re likely to build as it’s the cheapest (and can produce more anima for you).
Other buildings: The anima conductor lets you select an area in your zone that will have extra things for you to do when you channel anima there. It’s 25 anima that you can spend once a day, and after you do it 10 times you can make one of the channels permanent. The first 2 choices are a chest to open or a named mob to kill. It’s usually a net gain of anima if you go do whatever you open up, and not useful if you don’t. The transport network makes it easier to get around the zone, the first unlock will open a few transports, the next more, etc. It may open up additional content to do as well.
Finally, each of the covenants has a unique building. These primarily produce pets, transmogs and the like. All of them have something to commend them, but they are purely optional.
Each covenant has a set of armor. The pieces are awarded as you progress in the story quests. As your renown increases, the ilvl of the armor increases. There is a “Advanced Armor” NPC in your covenant that will upgrade older pieces to whatever the new ilvl is for a small amount of anima. If you’re at the max this week for covenant renown, the ilvl is 184, the same as mythic drops, so it can be quite worthwhile. If you sold one of the pieces, you can also buy a copy for anima.
Covenants have a lot of transmog items available for anima. Be warned, the hearthstone they offer is just a ‘transmog’ for your hearthstone—it does not give you a second hearthstone to your covenant.
At various renown levels, the ilvl of the drops you get from world quests increases. At another renown level, the ilvl of pvp items is increased.
Each day a new calling is available in your covenant. These are a lot like the Emissaries of BfA, with the exception that you have to go to your covenant to pick it up before you do it. (You still have to go back to turn it in.) You can have up to 3 callings available. Every covenant gets the equivalent calling each day—if yours sends you to Bastion, all of them will send everyone to Bastion. This makes it possible to group up to do things even if your friends are in different covenants.
There are three kinds of callings. One requires doing 3 world quests. One requires ‘defending’ the zone—this can be done by 4 world quests or some combination of world quests and opening treasure chests. The last requires doing either one of the two dungeons in the zone or an elite quest (the group finder will usually have groups doing the elite quest).
If you are behind in renown, callings will usually offer an increment of renown. This is the main catch-up mechanism. Each calling awards a chest and reputation for whatever zone it was in; you no longer get to see if the reward is something you want to do. The chest always contains some grey items worth about 2000 gold and may contain an item or a conduit.
Each week, the Covenant will have a quest to retrieve souls from the Maw (used in making/upgrading the Sanctum buildings) and a quest to recover 1000 anima. Both of these quests give renown. In addition there will be a third quest with some bit of story advancement and a renown point, and several of the other buildings may have quests. You can always earn a minimum of 3 renown per week (until we hit 40). I've found the stories I've done so far to be quite interesting and different between covenants.