A logo is a simple design that represents a company, organization, or product. Your college might have a logo composed of a picture of your mascot in your school colors.
Just about any company you can think of has a logo, whether it's Apple and its apple or Coca-Cola and its signature red Coke bottle lettering. A logo is meant to immediately convey what the brand is and be memorable enough that you'll think of that brand every time you see the logo. The word has been around since the 1930's, when it's thought to have been shortened from logogram, which combines the Greek logos, "word," with gram, "something written."