A Binding Vow (縛り Shibari?) is a pact made with jujutsu that creates conditions for themselves or agreements with others.
Binding vows are considered by all cursed energy users to be one of the essential tenants of jujutsu sorcery. They are essentially contracts created through cursed energy that an individual can make with one's self or another person. The act of abiding by the rules and restrictions agreed upon in these contracts can result in a greater power or the achievement of a goal, but breaking a binding vow has uncanny repercussions. 
Vows with Oneself
Self-imposed restrictions that are potentially harmful to the creator, such as willingly limiting the amount of Cursed Energy they can use for a period of time, can increase the amount of the user's cursed energy and of their cursed techniques.
As a product of negative emotions, cursed energy responds to the desires of its individual user. As a result, the user can increase the power of their cursed energy by stating a self-imposed "Cursed Restriction" that creates riskier conditions to use their abilities. For example, by divulging one's cursed technique, it creates more risk for them, making their cursed energy swell in response to its user's resolve.
In addition, creating rules for using one's cursed energy and abiding by those rules which allow their cursed technique to improve in strength. The penalty of breaking a binding vow with oneself is the loss of whatever was gained through the contract. 
Showing One's Cards: A Binding Vow that increases the user's cursed energy in exchange for vocally divulging how their cursed technique functions.
Overtime: A Binding Vow used by Kento Nanami that limits the amount of Cursed Energy he can access while on the clock working for Jujutsu High. Once his normal shift ends and he begins working overtime, Nanami's Cursed Energy increases dramatically.
Vows with Others
Contracts created between two or more individuals are bound by Cursed Energy. Both parties must agree to a particular set of conditions that benefit both parties. The penalty for breaking a Binding Vow with others is considered to be far greater than that of a self-imposed Binding Vow. 
Yuji's Revival: When Yuji's body was deceased, Sukuna proposed a Binding Vow that would allow him to heal in exchange for allowing Sukuna to take control for one minute whenever he said a keyword. He also promised not to kill anyone during that time on the condition that Yuji would forget about the vow.
Yuji initially refused and demanded a fight to death in response. As a compromise, conditions were set by Sukuna. If Yuji wins then Sukuna will revive him without the Binding Vow. If Sukuna wins, then Yuji must agree to the Binding Vow and will lose all memory of it. Sukuna instantly defeated Yuji, forcing him into the vow.
Jujutsu High Mole: A contract between Mahito, Suguru Geto, and Kokichi Muta for Muta to act as a double agent for Mahito and Geto. Mahito and Geto agreed to heal Muta's body with Mahito's cursed technique in exchange for cooperation and information, on the condition that Mahito and Geto would not "lay a finger on anyone from Kyoto Jujutsu High."
It is alleged by Muta that this contract is broken, but Mahito rebuts this point by stating that Hanami actually was the one who hurt the students from the Kyoto College. Muta is transformed by Mahito's cursed technique after acting as a double agent for presumably some time, which brings the contract to an end, although it is unclear whether there was a breach.