It's not just jets. WW2 bombers, B17s and the like, also left contrails when they were on high altitude runs. Combustion produces water vapor, which under the right conditions condenses into a cloudlike trail of visible water droplets.

Contrails (water vapor condensation) can also form in wingtip vortices or propeller tips especially when pulling high G loads (high angle of attack accelerated turns) IIRC they happen in these contexts as the low pressure area over the wing (or prop) grows and the low pressure air can't hold as much water vapor as higher-pressure air can, so the relative humidity increases eventually to 100% of capacity at which point the H2O vapor condenses out as droplets.

Mike