Commodore International, also known as Commodore Business Machines (CBM), was a computer company that manufactured some of the best-selling computers of the early-to-mid-80's, including the Commodore 64, perhaps the most well-known (and certainly best-selling) computer of the 80's, and the Amiga, a popular workstation computer. (See also AmigaOS.)
For a complete history of Commodore, see Wikipedia's Commodore page.
Recently (since 2010), a new company, Commodore USA, licensed the Commodore and Amiga brand names to sell modern PCs with the form of the classic Commodore 64 (i.e. an all-in-one computer, with the "keyboard" also containing the processor, hard drive, various communication ports, etc.), along with another all-in-one using the VIC brand name (but not the form) and 2 "Amiga" systems.