Complex sentence: The Crickets was the name of Buddy Holly's rock and roll band, while Holly's home town baseball team in the Texas-Louisiana League was called the Lubbock Crickets.
Split into simpler sentences: The Crickets was the name of Buddy Holly's rock and roll band. In Lubbock, Texas, Holly's home town, a baseball team in the Texas-Louisiana League were called the Lubbock Crickets.