Codex in Diablo Immortal lets you complete different quests and dungeons to earn Battle Points and progress your Battle Pass. These are separated into four categories: Guide, Battle Pass, Activities and Exploration.
Guide is most similar to Diablo III's Season Journey. You can complete a variety of miscellaneous objectives such as completing bounties, finding or salvaging certain items, or just inserting gems into socket. Each objective gives you a small reward on completion. Additionally, these objectives are grouped into Chapters and you get more rewards and Battle Points when you complete all objectives in a Chapter.
Battle Pass itself consists of two parts: Quests and Rewards.
Quests are granted every few days when the season is active and you have until the end of the season to complete them.
Rewards are basically the centerpiece of the entire Codex. Everything you do in here gives you Battle Points which are used to rank up your Battle Path. On each new rank you receive rewards all the way up to rank 40. After that you can receive a Gift of Renown for every 180 Battle Points earned (up to 20 times per season). Additionally, you can purchase the Battle Pass to increase the reward earned on each rank.
Activities can be repeated for Battle Points up to a maximum cap every week. This cap is reset every Monday. Activities themselves can refer you to some other part of the game, such as Bounties or Elder Rifts, or be a separate instanced Dungeons with unique objectives.
Exploration gives you a bunch of objectives to complete in each of the World Zones. These objectives are similar to Achievements in Diablo III: kill some enemies, elites or bosses, complete unique events and discover the map itself.