The Champions of Azeroth are a very important faction in BfA, since each new reputation level will give you bonus item levels to your Artifact Necklace Heart of Azeroth. Both Friendly, Honored, and Revered gives you an additional 15 bonus item levels, and you need to claim these by going to Silithus and doing a talking quest with Magni to get it.
Getting reputation with Champions of AzerothThe main way to get reputation with Champions of Azeroth is by doing World Quests. In contrast to many of the other factions in Battle for Azeroth, the Champions of Azeroth are not tied to a single zone, but can instead spawn World Quests in any zone (much like The Wardens in Legion). Basically any quest that involves Azerite will give 125 reputation with Champions of Azeroth. There are also no real quest chains that give reputation with Champions of Azeroth, so you need to get it all from other sources.
The Champions of Azeroth can also have an Emissary Quest up, where you will get an additional 1,500 reputation by completing 4 of their World Quests. Each new day will get a new random Emissary Quests, and make sure to do this before the 72 hour timer is done if you want the bonus rep (the a bonus chest with a chance for some nice gear).
You can also use the item Contract: Champions of Azeroth to get an extra 10 reputation with Champions of Azeroth any time you complete a World Quest (with any faction). This item lasts forever, but you can only have one faction contract at a time. The item is made by the profession Inscription, and can be bought on the Auction House. Keep in mind that you need to be Friendly with Champions of Azeroth to use it, so you will need to get some rep before you can use this.
A final way to get rep with Champions of Azeroth is from the Mission Table, where you do follower missions. Some of these can award the item Champion of Azeroth that gives 150 reputation. This is BoP, so you cannot farm it on alts like you could in Legion.
Champions of Azeroth reputation rewardsIn addition to giving 15 item levels to your Artifact per reputation level (except for at Exalted), the faction sells the following items:
Drape of the Azerothian Champion - ilvl 320 cloak
Drop of Azerite - Azerite Puddle pet
Shard of Azerite - Azeriti pet
Azerothian Champion's Crown - ilvl 355 cloth helm
Vest of the Azerothian Champion - ilvl 355 leather chest
Azerothian Champion's Spaulders - ilvl 355 mail shoulders
Helm of the Azerothian Champion - ilvl 355 plate helm
Champions of Azeroth Tabard