The Atmosphere of the Earth consists mainly of Nitrogen, Oxygen, Argon and Carbon dioxide. Increased carbon dioxide and increased methane leads to Global warming. The atmosphere has different layers, the lowest layer is called the troposphere and is where Humans, Animals and Plants live. The troposphere is also where clouds, Rain and all weather systems happen. (The biosphere is similar to the troposhpere but includes the Earth's surface, also lakes, rivers, Seas and Oceans, and even a bit of the upper atmosphere, anywhere where there are living things.)   The upper atmosphere above the troposphere is also important because it shields life from harmful radiation and human made pollutants have reduced its ability to do that.  
The atmosphere of any Planet is a shell of gasses surrounding that planet and kept in place by that planet's Gravity. Many planets have atmospheres, the Gas giants have very thick Atmospheres.You'd expect that because they're called gas giant. Gas giants in the Solar System have unbreathable atmospheres with poisonous gasses like methane, Hydrogen and ammonia. We couldn't live there anyway because those planets are too cold.