The white stripes that you have surely seen before are called vapour trails. Vapour means that a substance turns from being gaseous to being liquid.
Plane exhaust contains steam and soot particles. When the hot exhaust gases leave the engines they mix with the cold air and condense into tiny droplets. If the air is cold enough, namely at least minus 40 degrees Celsius, they freeze into small ice clumps.
When these ice clumps collect together we see them as white stripes in the sky. Because they are made up of the frozen, vaporised exhaust gases, we call them vapour trails.
If there is no wind you can see how the vapour trails stay in the sky for a very long time. If a plane doesn't leave any vapour trails in the sky it is because there is not enough humidity. If the air is dry, the water condenses quickly and the ice crystals cannot form. Get some binoculars and take a closer look at the vapour trails. You'll notice that they never start right behind the plane, because to become visible for us lots of ice crystals have to gather together. That can take a little while.