A two-variable graph typically refers to a function of two variables, represented as z = f(x, y), which requires three axes: x, y, and z. This type of graph visualizes how a height (z-value) changes based on pairs of x and y coordinates, often depicted in three-dimensional space. The discussion also touches on terminology, clarifying that while "two-variable graph" is not standard, it can refer to different contexts, including statistics and coordinate geometry. Level set curves, which represent constant values in a two-variable function, are mentioned as a related concept. Overall, the conversation emphasizes the need for clarity in terminology when discussing two-variable graphs.