https://www.crosswalk.com/slideshows/10-disney-movies-with-secret-christian-messages.html
https://en.wikipedia.org/wiki/Religious_denomination
Covenants are "factions" within Dark Souls and Dark Souls Remastered. To join a covenant the player must make oaths to specific NPCs. With each covenant there are rewards for following the guidelines set by your "leader" and there are penalties for breaking them. Covenants may also have an effect on the player's online interactions. There are nine covenants total.
Most covenants have a unique multiplayer item useable only by members of that covenant, and even the ones that do not will have items or spells that can affect other players in some way, and as such what covenant the player has joined will have an effect on the player's online experience. Generally speaking, each covenant will focus on either cooperation (summoning/being summoned) or competition (invading/being invaded), but even then how the player chooses to play the game is still their choice. As an example, a player in the Warriors of Sunlight covenant (which emphasizes co-op pve) could be in the covenant purely for the ability to cast the Sunlight Spear miracle, and use Cracked Red Eye Orbs (an invasion item available to all players regardless of covenant) so that they may invade other players and use the miracle on them!
"The setup for the various covenants affects multiplayer situations in many different ways, especially the parameters of versus play, expanding the scope well beyond Demon's Souls. The game is designed to introduce multiplayer events as an extension of each character's role-playing in these covenants." []
Note: for the achievements you don't need to join them, once you get the dialogue that let you choose whether you want to join, the achievement will pop up.