Those long white lines behind high-flying airplanes are called contrails, short for condensation trails.
They form because jet engines produce water vapor as part of combustion.
High in the atmosphere, the air can be extremely cold.
Warm exhaust meets cold air
Hot exhaust leaves the engine carrying water vapor.
When that warm, moist exhaust mixes with the cold surrounding air, some of the water can condense and then freeze into tiny ice crystals.
Those crystals form the visible white trail.
A contrail is basically an artificial cloud
The ice crystals scatter light, so you can see them from the ground.
In that sense, a contrail behaves much like other collections of tiny atmospheric water particles.
That connects it to why clouds can stay suspended in the sky and why fog is visible.
Why do some contrails vanish quickly?
Humidity matters.
If the surrounding upper air is relatively dry, the ice crystals may disappear quickly.
The trail may last only seconds or minutes.
Why do other contrails spread out?
If the surrounding air is humid enough, the ice crystals can persist.
Winds can stretch and spread the trail.
A contrail that began as a narrow line may become much wider.
Why can two airplanes leave different trails?
They may be flying through air with different temperature and humidity.
Even small changes in altitude can place an airplane in a different atmospheric layer.
So one jet may leave a long-lasting trail while another nearby leaves almost nothing.
Is the trail smoke?
Not in the ordinary sense.
Jet exhaust contains combustion products, but the bright white line you see is mainly a cloud of tiny ice crystals formed in the cold upper atmosphere.
The airplane did not draw a white line in the sky.
It briefly helped make a cloud.
And that’s the short explanation.
Related explanations: Why do clouds stay in the sky?, Why does fog form?, and Why can you see your breath in cold weather?