Hanshin is the name of the industrial region on Osaka Bay
: its name comes from the middle characters in "Osaka-Kobe" (大阪神
More frequently, Hanshin refers to any number of holdings of the Hanshin Group, which got its start in the early 1900's as the Hanshin Railway, a railway line between Osaka and Kobe. The Hanshin Railway now runs from Umeda in Osaka to Sannomiya and Motomachi in Kobe, stopping at Noda, Amagasaki, Koshien, and Ashiya along the way. (If you're going straight from Osaka to Kobe, it's faster and cheaper to take Hankyu instead.)
Since then, the Hanshin Group has dived headfirst into other businesses. They own the Hanshin Tigers, the region's favorite, if underdog, baseball team. They also own a chain of department stores (just as Hankyu and Kintetsu do), an extensive bus network, a real estate agency, a helicopter line, and a ski resort on Mount Rokko.