Planes have changed a lot since the days of the Wright Brothers. Those first wood and cloth contraptions are an entirely different species than the sleek Boeing Dream liners of today. With the continual advancements in aerospace technology, it is hard to keep up with all the amazing things this planes can do.
Jets leave white trails in their wake for the same reason you can sometimes see your breath. The hot, humid exhaust from engines mixes with the atmosphere, which at high altitude is of much lower vapor pressure and temperature than the gas.
In sort, the contrails as they are populary known, are formed in the exhaust from the plane's engines condenses into water droplets, which then freaze into ice particles composing a line shaped cloud. The impurities in the jet exhaust form some of the particles in which water droplets grow, before freezing.
Exhaust contrails usually form at high altitudes, above 8,000 metres, where the air temperature is below -36.5 Degrees Celsius. They can also form closer to the ground when the air is cold and moist. Cirrus clouds form a few minutes after the plane has passed and usually last a few minutes or hours.