A sheaf is a mathematical concept used in the field of topology and algebraic geometry. It consists of a collection of data that is organized in a way that allows for local information to be combined into a global perspective. Each piece of data is associated with an open set in a given space, and the sheaf provides rules for how to piece together this local information. In simpler terms, think of a sheaf as a way to keep track of information that varies over different parts of a space. For example, if you have a map of a region, a sheaf can help you manage the details of that region, like the temperature at different locations, ensuring that you can understand the overall climate by looking at local data.