An ordered pair is a mathematical concept used to represent a relationship between two elements. It is written in the form a, b, where a is the first element and b is the second element. The order of the elements is important; changing their positions creates a different ordered pair. For example, 3, 5 is not the same as 5, 3. Ordered pairs are commonly used in coordinate systems, such as the Cartesian plane, where the first element represents the x-coordinate and the second element represents the y-coordinate. This allows for precise location identification in two-dimensional space, making it essential in fields like geometry and graphing.