Planes are defined as two dimensional flat surfaces that have width and length but no depth.

The graph on the left is two-dimensional. All points in this graph are in the xy-plane which is formed by the intersection of the x-axis and the y-axis. The grids shown on this graph show the x-axis and the y-axis intersection at the point (x,y) = (0,0).

The graph on the right is three-dimensional. All points in this graph are formed by the intersection of the x-axis and the y-axis in the xy-plane, the x-axis and the z-axis in the xz-plane, and the y-axis and the z-axis in the yz-plane. The grids on this graph show the x-axis and the y-axis and the z-axis intersection at the point (x,y,z) = (-5,-5,-5). The intersection point will change if the low end of the range of each axis changes. This is not the true center point of the graph. The true center point of the graph is at the point (x,y,z) = (0,0,0) which is not shown.

This can cause some difficulty in perception until you get used to it. Forming the grids this way has some advantages in making the objects easier to see without axis grids getting in the way. The disadvantage is that you don't see the true zero point on the graph unless you construct your own axis grids that intersect at the point (x,y,z) = (0,0,0).

Please note that showing the axis grids this way is a function of the graphing tool I am using. There are other graphing tools on the market that show them differently, while still others might show them the same.