The major new mechanical system in Battle for Azeroth is Azerite Armor. It's kind of a cross between Legion legendaries and artifact weapons. Like artifact weapons, you empower your neckpiece by collecting Azerite Power. Then your head, shoulders, and chest are special pieces which have abilities that unlock based on your Azerite level. You can usually choose one ability from four or so choices.
There are three or four rings which can be unlocked. The first ring has abilities which modify your powers. The second-last ring has defensive abilities, and the last ring gives +5 item levels. Raid gear has a second outer ring with offensive passives.
However, unlike legendaries, it's not a completely random system. Specific pieces have specific abilities, so you can farm exactly the abilities you want. Azerite pieces also don't warforge, so you don't have to worry about getting a better version.
It's not a bad system, but it isn't a great system either.
The greatest flaw is that it's not an exciting system. It's a very "Spike" system, to use Magic: the Gathering terminology. A Legion legendary drop was an event. It was rare, and was raw power compared to normal gear. The only problem was that some legendaries were much more valuable than others. A similar thing happened with Artifact weapons. Getting one was another event, and then you unlocked this giant tree of abilities which you worked on filling out. The anticipation of having a completed weapon was very attractive.
Compared to those systems, Azerite Armor lacks sizzle. Most of the power is in that first ring, so it's very front-loaded. The final reward, +5 item levels, is useful, but rather boring.
The other issue with Azerite Armor is that there is a corner case which is a bad experience if it happens to you. If your necklace is behind on Azerite levels, and you loot a very high ilevel piece, none of the rings are unlocked, and the armor feels useless. It's not quite as bad as getting the "worst" legendary, though. Your comparative power to other players is still the same, and you can leave the armor in your bags until you achieve the required level and you've got an instant upgrade then.
For the most part, though, I think Azerite Armor will play well. It will give players something achievable to chase, kind of like set gear, but without the massive gap between those who have the item and those who don't. It's also different from normal armor, where you chase secondary stats. You also get to collect different sets of Azerite Armor for different specs, but you can get by with only those 3 pieces (and trinkets and weapons).
It's just a very boring system, compared to the pure excitement of the Legion gear systems. Azerite Armor may very well be better in day-to-day play, though. It might have been better received if Azerite Armor had been the mechanic for the next expansion, to put some space between it and Legion.
1. "Spike is the competitive player. Spike plays to win. Spike enjoys winning. To accomplish this, Spike will play whatever the best deck is. Spike will copy decks off the Internet. Spike will borrow other players’ decks. To Spike, the thrill of Magic is the adrenalin rush of competition. Spike enjoys the stimulation of outplaying the opponent and the glory of victory."