The atmosphere is thin and cold the higher up a plane goes. The exhaust from a plane's engine is much hotter than the atmosphere. The water vapor from the hot plane engine turns to ice mid-air which we see as white lines in the sky called contrails.
This is the same phenomenon we see when we breathe hot air on a cold day. Long contrails form in humid conditions while short contrails form in low humidity. Long contrails are a sign a storm may be coming. Short contrails are a sign fair weather is coming.