When you have the buff from having used a Contract, you will get 10 extra reputation with the chosen faction each time you complete a World Quest. It can be absolutely any level 120 World Quest (so no use going back to the Broken Isles), so it's a nice way to farm rep with a specific faction without having to wait for their World Quests to pop up. It's still very slow though, since you need to do 100 WQs for only 1,000 rep.
Each contract is tied to one of the Battle for Azeroth factions, and all of them (except for 7th Legion for Alliance, and The Honorbound for Horde) has a Contract for their faction. This leaves us with the following 8 Contrats:
Neutral factions:Contract: Champions of Azeroth
Contract: Tortollan Seekers
Alliance factions:Contract: Proudmoore Admiralty
Contract: Order of Embers
Contract: Storm's Wake
Horde factions:Contract: Zandalari Empire
Contract: Talanji's Expedition
Crafting a reputation contractYou need Inscription BfA level 95 for Rank 1, 105 for Rank 2, and 115 for Rank 3 to create any of the reputation contracts. It's a nice way to level up Inscription, since this is likely to be an item that will be valuable and sell a lot.
To create any of the contracts, you need the following items:
Rank 1: 18 Ultramarine Ink + 10 Crimson Ink
Rank 2: 15 Ultramarine Ink + 8 Crimson Ink
Rank 3: 12 Ultramarine Ink + 5 Crimson Ink