Which layer of the atmosphere gets warmer with altitude, trapping the one below it?

The stratosphere, which is warmed from above rather than below: ozone absorbs ultraviolet, so temperature rises with height instead of falling. That inversion is the important part, because warm air over cold air does not rise, so the layer is extremely stable and does not churn.

Everything follows from that. Weather is confined to the turbulent troposphere underneath, and thunderstorms flatten into anvils when they hit the boundary because they cannot punch through. Airliners cruise just at the lower edge for the smooth air. And anything that does get into the stratosphere stays for years, which is why a large volcanic eruption cools the planet for a season or two and why CFCs had time to reach the ozone layer and destroy it.

It is also where the coldest natural temperatures on Earth are found - not at the poles on the ground but at the boundary above the tropics, around minus 80 Celsius, because that is where air has risen highest and expanded most before the ozone warming takes over.