This is a term used in sports, including professional baseball, which describes a rivalry rooted in geographic proximity. Teams in all sports have rivals for various reasons, such as one team beating the other consistently or a bad trade between the two. So-called "crosstown rivalries" are among the most popular forms of rivalry because they are easy to form. Major League Baseball is infamous for transplanting the New York Giants and Brooklyn Dodgers rivalry out to the West Coast (San Francisco and Los Angeles, respectively) in order to increase interest in baseball in new markets.
This term is used in almost every sport, at almost every level. College teams are especially prone to crosstown rivalries because schools are more numerous than professional teams; there is always another school close by. Before air travel became a viable option for professional teams, teams typically played those closest to them the most. This was a matter of practicality; a team simply could not make it to the West Coast and back in a week. As a result, the teams they played the most would become the most familiar-resulting in the best games, which fans and players enjoy.