Slice a surface at every height and watch its topographic map appear. Crowded lines mean steep ground.
Drag the left panel to turn the surface. Both panels always show the same function.
Drag the height slider, or drag on the surface to turn it.
A function of two variables is a landscape, and a landscape is awkward to draw. So cartographers do something clever: instead of drawing the hill, they draw the level curves — slice the surface at a series of evenly spaced heights and trace where each cut lands.
That is exactly what the plane on the left is doing. Slide it up and watch the curve it carves appear on the map at the right. Everything the map knows about the hill is captured by that family of curves.
Now the part worth slowing down for. The heights are evenly spaced, but the curves are not. Where the ground is steep, you climb through several contour heights over a short horizontal distance, so the curves crowd together. Where it's nearly flat, one contour drifts far from the next.
So contour spacing is steepness. That's why hikers can read a topographic map at a glance, and it's the reason a hand-drawn contour sketch with evenly spaced rings is wrong — on the bowl, the rings must crowd as you go out, because a bowl gets steeper the further you climb.