You might want to look at the
Contrailb altitudes thread for some informaiton and some links to other sites.
Basically, when you burn fuel you get a bunch of gasses, mostly carbon dioxide and monoxide, some sulfides and others, but one of these gases is water vapour.
If the air is cold enough, and not too dry, then when the exhaust hits that cold air, the water vapour condenses into water, which then freezes into ice crystals, forming a contrail.