Definition
A contour line is an imaginary line that connects points of equal height above average sea level. On flat paper or a screen, it lets you see a mountain's height, how steep its slopes are, and the shape of its valleys at a glance.
How to fit a 3D mountain onto 2D paper
Imagine a cone-shaped mountain made of clay. You slice it into thin, evenly spaced layers and look down from above. If you trace the edge of each slice on paper, you get round rings of different sizes stacked inside each other. That is the basic idea behind contour lines.
The most useful clue on a contour map is the distance between lines. On a steep spot like a sheer cliff, the height climbs fast over a short horizontal distance, so the lines are packed very close together.
On a field or a gentle hill, the height changes slowly, so the lines are spread far apart. In other words, just by checking how crowded the lines are, you can guess ahead of time whether a walk will be hard or easy.
Ridge or valley: how can you tell?
Contour lines tell you more than how steep a mountain is. They also show how its bumpy skeleton is laid out. Look closely at a map and you will see that the lines do not only form circles. In some places they zigzag or bend into V shapes.
If the point of a V pushes uphill, toward the peak, that spot is a valley where water flows. Rainwater runs from high ground to low ground at right angles to the contour lines, so it gathers there.
If the bend instead points downhill, it marks a ridge, a strip of ground that stands higher than both sides and is often good for walking. So with contour lines, you can tell the valleys where water collects from the ridges that rise above their surroundings, all before you set foot outside.
A bit more precisely: regular and index contours
If you unfold a map, you will notice that not all contour lines are drawn with the same thickness. Every so often, a thick, dark line appears among the thin ones, with a number like "100" or "200" printed on it.
The thin lines are the basic ones, called regular contours. Every fifth line is drawn thicker so you can read heights easily. These are called index contours. In Korean, the term is gyegok-seon, which means "a line for counting height" and has nothing to do with the similar-sounding word for a valley. Without the thick lines, you would have to count the crowded lines one by one with your finger to work out the height.
To be more precise, the real height between one line and the next depends on the map's scale, which is the ratio by which the real world is shrunk. On a 1:50,000 map, each thin line stands for 20 meters of height. On a 1:25,000 map, a line is drawn every 10 meters, which shows the terrain in much finer detail.
Common misconceptions
Contour lines are actually drawn on the ground.
Contour lines are imaginary lines that mapmakers use to show the ups and downs of the land on a map. No lines are actually drawn on a real mountain or field.
When the terrain gets complicated, contour lines can cross each other in an X shape.
A single point cannot have two different heights at once, so contour lines normally never cross. On a vertical cliff they merge into one line, and on an overhanging cliff, where the top sticks out, they can cross as a rare exception.
Where you meet it
When you look at a hiking trail map, you can skip the rough route where the contour lines are packed tight and pick a gentler path.
On a weather map, "isobars" connect places with the same air pressure to show how wind flows. They work on exactly the same principle as contour lines.
In one sentence
Contour lines are imaginary lines connecting points of equal height. The closer together they are, the steeper the slope, and the farther apart, the gentler it is.