The Action Lab's James Orgill writes, "In this video I show you how it is possible to contain the fire from a burning ball of propane in a wire mesh." Yes, it is possible. But that doesn't mean you should do it. In fact, you shouldn't.
The experiment demonstrates the phenomenon behind the Davy Lamp, a lamp that Sir Humphry Davy invented in 1812 for use in coal mines. From Wikipedia:
The lamp consists of a wick lamp with the flame enclosed inside a mesh screen. The screen acts as a flame arrestor; air (and any firedamp present) can pass through the mesh freely enough to support combustion, but the holes are too fine to allow a flame to propagate through them and ignite any firedamp outside the mesh. It originally burned a heavy vegetable oil.
The lamp also provided a test for the presence of gases. If flammable gas mixtures were present, the flame of the Davy lamp burned higher with a blue tinge. Lamps were equipped with a metal gauge to measure the height of the flame. Miners could place the safety lamp close to the ground to detect gases, such as carbon dioxide, that are denser than air and so could collect in depressions in the mine; if the mine air was oxygen-poor (asphyxiant gas), the lamp flame would be extinguished (black damp or chokedamp). A methane-air flame is extinguished at about 17% oxygen content (which will still support life), so the lamp gave an early indication of an unhealthy atmosphere, allowing the miners to get out before they died of asphyxiation.