Well, it’s usually caused when planes reach a really high altitude. The white trail can be smoke, water vapor, or heated exhaust reacting with the cold humid air at those high altitudes, creating a mini cloud. It does go away because the vapor cools back down and dissipates back into the air.
However, there is a conspiracy called the chemtrail conspiracy theory that suggests that some trails left by aircraft are actually chemical or biological agents deliberately sprayed at high altitudes for a purpose undisclosed to the general public in clandestine programs directed by government officials, changing the weather, say some. You can do your own research to find out.