Spinning objects have angular momentum, a vector quantity that is conserved in absecne of external torques.
If a bullet is spinning along its axis, the angular momentum will point towards the front of the bullet, and since no external torques act on it, the angular momentum won't change, causing the bullet to keep the same orientation.
Keeping the bullet oriented in the direction to which it was initially moving will help avoiding air drag. Air drag can cause the bullet to slow down or change its trajectory. Thus, the bullet would travel farther and more accurately if it is spinning around its axis.