Professional baseball team (National League) who played at Ebbets Field
in New York
city until 1958. That year they left the borough of Brooklyn
and moved to the west coast
to play in Los Angeles
. The name "dodgers" came from the term used to describe people who jumped onto/off of streetcars in the city.
Their chief rival, the New York Giants baseball team, played across town until they too moved to California. The San Francisco Giants also left New York prior to the '58 season.
some information from sfgiants.com