On a topographic map, the contour lines follow a certain elevation across the terrain. So here's what each of the things you mention would mean:
If the lines are far apart, that means that there is little or no slope in that area of the map. When the lines are far apart it means that there's a long horizontal distance between places with different elevations.
By contrast, if the lines are close together, that means there is only a short distance between places with different elevations. That means it's a steep slope.
If the lines are practically touching, that means it's a very steep slope -- maybe even vertical.
On the second link provided, scroll down to "Contour Lines."
It shows the degree of elevation from the ground.
Contour lines on a map connect all the points with same elevation elevation or fight of the land. The way these contour lines are determined and shown on the map. any two neighbouring lines represent a fixed difference in the heights represented by them. Depending on the scale of the map and the number of contour line drawn to cover the total area of the map, the difference in elevation between two contour lines may vary between less than a meter to several hundred meters. But for a given map it is always same.
Therefore when the distance between two contour lines is more it shows that the fixed difference in elevation of the places represented by the contour lines is reached over a longer distance. This is same as saying that average slope or gradient between the two contour lines is low. In contrast when the contour lines are closer together they represent high gradient or slope. Two contour lines touching each other represent a vertical gradient or fall.