Heart of Azeroth is an all-new Artifact necklace in WoW patch 8.0, which could gear up Heart of Azeroth in the whole patch Battle for Azeroth. This is the new Artifact Weapon, and Azerite will be the new Artifact Power.
When you reach level 110 and complete some quests, you will be rewarded with the artifact neck Heart of Azeroth.
Azerite power will be automatically added to your Heart of Azeroth whenever Azerite is obtained. Gaining enough Azerite eventually levels up the Heart of Azeroth, and when it reaches certain level, it will unlock Azerite Traits on specific pieces of gear called Azerite Armor. You can farm Azerite by completing World Qquests, Island Expeditions, and Mythic+ runs, and the amount of Azerite Power needed to increase each level of Heart of Azeroth will gradually decrease as time goes by.
The Heart of Azeroth is directly connected to your head, shoulders, and chest item slots. Each of these items have tiers that you can progressively unlock when your Heart of Azeroth receives enough Azerite and ranks up.
The item level of Heart of Azeroth will upgrade as you gain new ranks of reputation with the Champions of Azeroth and higer level of Heart of Azeroth, when you upgrade one level, such as reaching friendly, you will receive the quest The Heart's Power and increase your necklace’s item level by 15 levels. And as the necklace upgrades one level, the item level of it will upgrade 2 levels.
The level of Heart of Azerite makes a great difference to the average item level, you'd better grind as much reputation as possible, and do more quests to upgrade the level of Heart of Azeroth if time permits.