Other than wood firing which can create a natural ash glaze, another type of atmospheric firing is when ceramicists add salt to the kiln while firing it. Regular ol’ salt, which is sodium chloride, is introduced into a kiln when it’s very hot (around 2250 degrees).
At this high temperature, soda or sodium breaks away from the salt molecule and combines with the silica that’s present inside the kiln; which is basically in everything as well as being one of the main ingredients in clay; to create an atmospheric glaze called a sodium-silicate glaze (This may be more technical than you wanted but a lot of things happen in ceramics on a chemistry / molecular level). This sodium-silicate glaze is the most basic of glaze recipes. Because of the way the salt is introduced into the kiln – usually as a paper wrapped envelope of salt that you throw in or dumped directly into the kiln on a metal channel, it’s not a uniform coating. The flame carries the salt, which vaporizes because of the heat, and gathers more thickly onto the sides of the clay that are closest to the firebox where the flames originate. As the flame carries the soda and chlorine vapor it gets less and less concentrated until it dissipates into the air as it exits the kiln chimney.
The other side effects of adding salt to a kiln firing is that (Note: Some of this is kind of technical…)

1) The chlorine is broken from the salt molecule and some of it combines with water vapor that’s present in the air to creates a diluted hydrochloric acid vapor, which goes up the chimney. In the kiln, some of the chlorine combines with different oxides in the clay's and glazes and can give pinkish tints as well as dark browns depending on what oxides are present.

2) The soda gives the glaze a very pronounced ‘orange peel’ texture depending on how much salt is added and how thick it collects on the surface, especially compared to soda firing, because of the way it gathers around the silica molecules.

3) Some flashing occurs – which is an intensifying of the yellows, red, and oranges - on many clay bodies but is less intense and bright then if it were a soda firing. Notice the foot of Hitomi Shibata’s piece.

4) It can also bleach out and/ or cause some colors or glazes that are used to run, giving the work a mottled and irregular coloration that adds to the individuality and uniqueness of the pieces.

Salt firing