Graphs are commonly used to simply plot a point. To locate the point, the measures along an x-axis and a y-axis are given. The expression may look like (x = 2; y = 5). This expression provides information about a point's coordinates on a grid. If you try to visualize it yourself, you have to imagine starting at the intersection of the x- and y-axis, moving two units to the right along the x-axis, then up five units along the y-axis. A graph provides this visual for you.
More than just points and coordinates, graphs can define spaces or areas. Any geometric shape can be defined with a graph by plotting three or more points and connecting the points with lines. Or, if they are connected with curves, the shape of the lines may be determined by a mathematical function sometimes called interpolation. Regardless of the shape or the kinds of lines that form the perimeter, graphs can define areas with distinct shapes. With simple coordinates, you may be able to envision the points or shapes. With more complex coordinates, graphing may be the only way to see what it looks like spatially.
Once an expression is graphed, rather than imagining what it would look like, you can study the relationships of the expression spatially. The information isn't presented in a sequence; it is presented all at once. This may make it easier to consider in different ways. An example of the benefits can be seen in graphing two objects to see if they overlap on a graph. This concept is used in computer-aided drafting to design parts, conceptually, without having to build prototypes.
Graphs aren't limited to two dimensions. A third axis can be introduced, allowing volumes to be displayed graphically. A volume doesn't just measure height and width but depth, too. The third axis can relate to other values. Regardless of the value each axis measures, three-dimensional shapes can be defined and represented graphically. It could be as simple as a cube or sphere, though it may be very complex.