What is it primarily used for and why is it so long?
It was late 19th century military round through WWII. The length of the 6.5mm bullets gave them a huge sectional density which gave them penetration that rivals and sometimes exceeds that of dangerous game bullets.
The funny thing about the length of the bullet is what has given Carcanos the mistaken reputation of being inaccurate. Earlier carcano rifles used gain-twist rifling (rifling gets progressively faster in twist rate from the breech to muzzle) and sometimes were cut down to shorter lengths to make carbines and no doubt cut down by bubba to make a deer rifle. When the faster twist portion of the barrel was cut off, the resulting rifle could no longer stabilize the long projectile leading to very poor accuracy. After Kennedy was shot with a Carcano, conspiracy wackos picked up on the idea of the 'inaccurate carcano' and the 'clunky carcano'- neither of which is true to those who have shot them.
FWIW, Finland purchased a large number of carcanos on 7.35 cal, and to put to bed the notion that carcanos were inaccurate, Finland had a much higher accuracy standard than the United States, Great Britain, or Germany at the time for acceptance of rifles for miliatry service.