Derby has many different meanings:

Various sporting events:

• horse race
• local derby (as in a game between two neighbouring teams)
• demolition derby
• roller derby
• Soap Box Derby

A hat:

• derby hat

The name of pottery factory in England and their china:

• Royal Crown Derby

It is also a place name:

• In Australia:
  • Derby , Tasmania
  • Derby , Western Australia
• In South Africa:
  • Derby, South Africa
• In the United Kingdom:
  • Derby, Derbyshire
• In the United States:
  • Derby, Colorado
  • Derby, Connecticut
  • Derby, Iowa
  • Derby, Kansas
  • Derby, New York
  • Derby, Vermont

(There is also Derby Line, Vermont and Darby, Pennsylvania.)