A coordinate system is a method used to uniquely identify points in a space using numbers. In a two-dimensional system, such as the Cartesian coordinate system, each point is represented by an ordered pair of numbers (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. In three dimensions, a third number (z) is added to represent depth. Coordinate systems can also be used in different contexts, such as in geography with latitude and longitude to pinpoint locations on Earth. They are essential in various fields, including mathematics, physics, and engineering, for analyzing and visualizing data.