Thematic Origin: Contracts are supposed to be the literal manifestation of how far humanity will go to achieve their goals, no matter how conceited or twisted the path may be to achieve it. It is one of the pieces of the puzzle of how the Curse Series was created.
In World Origin: Contracts are the gift given by the original Seven Deadly Sins to humanity in order to disrupt the gift given by the True God. Contracts allow the user to place conditions on their power to awaken a new power all together. They commonly were used in the world of RE:Alternative until someone was able to combine it with another ability to create the Curse Series.
Common Use: Contracts are now used as a way to artificially strengthen one's own Curse Pressure to limits beyond human comprehension. Most of the abilities of nobles have multiple contracts tied to their power. It is deeply discouraged from forming too many contracts, as a violation of a contract can lead to the user's Curse Pressure killing them as a result of it.