AG is short for Aktiengesellschaft. If you see the letters AG at the end of a German company's name, this means this is a joint-stock company, which trades shares on the stock market, and is owned by shareholders. The US equivalent is a 'corporation', or 'PLC' in the UK.
Literally translated, aktiengesellschaft means 'shares society'. The word is used for companies not only in Germany, but also German-speaking areas of Switzerland, Austria, Belgium and Luxembourg.
Unlike American or British companies that trade publicly, German AGs usually have two boards, a supervising board of directors, overlooking a management board who look after the company's everyday activities.
German AG companies include Axel Springer, Nero, PTV, Daimler, Gardena, Duetz and GfK. To learn more about how such companies work, watch this short film: