One character gives another character the power to totally wreck them, if they chose to.
Every human being requires a certain level of power to function. In order for politicians and cops to do their jobs properly, they have to be given certain levels of authority that, if abused, would have dire consequences. In more mundane circumstances, a boss has a large amount of authority over their subordinates and a teacher has the same over their students. This is why punishment is severe when said person in a position of trust abuses it, especially in cases of abuse or harassment. However, this trope is about people who are otherwise peers--friends, coworkers, siblings, neighbors, significant others--until one of them decides to give the other some type of power (whether a physical object, secrets, or money) that could completely screw them over if abused. It may be a Superhero that is a Person of Mass Destruction that lets the Five-Man Band know what their Weaksauce Weakness is, a Gentleman Thief who lets his Morality Pet know where he stashed his biggest heist, or a shy teenage girl letting her favorite, kind-hearted teacher know her biggest, darkest secret. Either way, they have completely put their future into this person's hands. The reasons for this are numerous; it's obviously a sign of trust, and the person giving away the power may want to indicate how much they believe in the other party. Another reason is to keep themselves honest: if they ever step out of line, make a Heel-Face Turn, become possessed or wind up Brainwashed and Crazy, they trust this person's judgment enough to do what needs to be done. These are only a few examples--the are a near infinite number of reasons why this can be done, including just for the fun of it. One type of this is telling someone else your Secret Identity or True Name.