When planes bank hard, they are subject to high load factors. All this means is that the wings are producing A LOT of lift. Wings produce lift by creating an area of low pressure on the top of the wing. If pressure drops rapidly, so does temperature. If you've ever used a hand-held air horn, you notice that the can gets ice cold when you release the pressure. The same thing is happening on the upper surface of the wing. The pressure drops (most notable in hard banks when the wings are producing the most lift), and the temperature drops to below the dewpoint, in essence creating a "cloud" or visible water vapor. This is the "smoke" that you see.
It happens on all types of fixed wing aircraft, especially in humid conditions. It is just water vapour in the atmosphere that condenses into visible "cloud" due to pressure drops lowering the temperature of the air as the wing cuts through it.
It can happen at any speed, and without the plane changing direction.
I second Coffeebuzz, and I'll add that irregularities in the surfaces of the aircraft such as hinge points, wing tips, lights, missile rails, etc, will collect said moisture, and lead it to condensing and streaming off. Vortices are the spiraling currents of air generated by the airfoil (escaping at the tip) that carry these vapors away.
I couldn't have said it better than Coffeebuzz. He is right. It will also occur if they do a quickly accelerated pitch up and the reason why it happens in a steep turn is because they are pulling back on the stick increasing angle of attack to to maintain altitude. The effect will vary with the relative humidity of the air.
First of all, it isn't smoke.
It's water vapors that have rapidly condensed on the surface due to friction, e.g. cold air rapidly moving over a warmer surface causes condensation.
Clouds of water. That water eventually evaporates and becomes vapor again.
Contrails
Wing tip vortices.
It's basically water vapor or condensation.
This is dust on the wings that the ground crew have failed to wash off when they were cleaning the plane.
