A contrail is the condensation trail that is left behind by a passing jet plane. Jet fuel is made of carbon and hydrogen, and when it burns, it combines with oxygen. So most of the exhaust is made of carbon dioxide and water. The water is usually an invisible vapor, unless the temperature, winds and humidity in the upper atmosphere are just right. Then white contrails form when the moisture in the exhaust condenses. It's similar to being able to see your breath when you exhale on cold days. Cold air can't hold as much moisture as warm air, so moisture condenses into a visible cloud. Temperatures at the high altitudes reached by jet planes are usually below -38 degrees Celsius.
There are three kinds of contrails: short-lived, persistent, and persistent spreading. Short-lived contrails resemble short white lines behind the plane. They only last 30 minutes or so, because there is so little moisture in the air that it quickly evaporates. Persistent contrails are long white lines that are still visible after the airplane has disappeared, because the surrounding air is full of moisture. Persistent spreading contrails resemble long, broad fuzzy white lines. They cover a larger area of the sky and last much longer than other types of contrails. So they are most likely to affect climate.
During World War II, bombers could be sighted from miles away because of contrails. But the accumulations were sometimes so extensive that pilots couldn't always find their targets, and sometimes collided with each other.