How do contour lines show steep and gentle slopes?

See explanation.

The spacing between contour lines reflect the slope. Very closely spaced contour lines represent a steep slope and conversely, widely spaced contours represent very gentle slopes.

Observe the contours around the mountain in the lower left quadrant of this example, the slope becomes very steep toward the top of the mountain. Near the lake on the right side of the map, the slope is more gentle.