An economic theory that (broadly speaking) argues that parties in a dispute about property rights can work things out in a mutually beneficial way without the intervention of some outside authority, like the government.
You and your sister both want the last cookie. Coase Theorem would say that you don't need to get your parents involved to solve the problem. Instead, the person who wants the cookie more will offer some sort of acceptable compensation for the cookie that will allow the dispute to get settled. Like...you might give your sister some of your Halloween candy instead, so she'll give up whatever claim she has on the cookie.
The theory was detailed by Ronald Coase, who laid out the theorem in a 1960 paper. The idea eventually helped him win a Nobel Prize.
There are some catches in the theorem, however. To work, the bargaining process itself has to be without costs, and there can't be any transaction costs related to the exchange. Furthermore, it only works if completely competitive markets are at play.