In the United States military, it refers to a group of 150-300 soldiers formed into three to six platoons, and typically commanded by a captain. Several companies form a battalion.
In the US and Canadian militaries (at least), individual companies are identified by letter - "B company", "company K", and so forth. The letters are often pronounced using the NATO phonetic alphabet or formerly the Joint Army/Navy Phonetic Alphabet, resulting in names such as Charlie Company and Easy Company, some of which have become familiar.