In two-dimensional geometry, the line represented by the equation y=0.

Actually, it's not necessary that the equation be y=0, but rather y=n, with n a constant. Further, in a polar graph, the x-axis is often the outer circle, and therefore the equation is r=n, where r is the radius and n a constant.

Really, the variable doesn't have to be x. The x-axis is where the independent variable is plotted. So one can see what happens as the independent variable varies. Time is often a good independent variable.

Some folks use the terms ordinate and abcissa to refer to the axes. Usually these folks are high school math teachers who have run out of interesting things to teach.