The Ducks usually refers to the University of Oregon football team. (See also ducks.) If you have just moved to Eugene, it is important to get used to saying "Go Ducks!" when other people start talking about their love of football and how the team is doing. You will see green and yellow signs, often with a large O, on many local businesses, people's cars, pretty much everywhere. People are obsessed and my advice is to just go along with it.
Also, don't wear orange or purple on game days or around fanatical Ducks.