If I was once observing this phenomenon in a plane I was sitting in (I am taking one tomorrow!), I would start to pray! No the motors of these airplanes aren’t exploding. These smoke-like, weird elongated swirls forming behind aircraft are so-called wake vortices and are particularly visible at high humidity.
Wake turbulence forms behind an aircraft as it passes through the air, creating wingtip vortices (longlived; shown in the video) and jetwash (shortlived; expelled gases from jet engine).
These horizontal tornadoes occur when a wing is generating lift. Air from below the wing (high pressure) is drawn around the wingtip into the region above the wing (low pressure), causing a vortex to trail from each wingtip.
As shown in the video, wake turbulences occur primarly during take off and landing.