"Ballistic Tip" is actually a trademark of Nosler, who first started making plastic tipped bullets in 1985.
Though originally designed to prevent damage to the bullet nose when feeding (while the nose of a soft tip or hollow point might deform due during feeding to the soft lead content in the nose, a plastic tip bullet will maintain a consistent nose shape) today the primary advantage of a polymer tipped bullets is a high ballistic coefficient. The design also allows the center of gravity to be moved back, increasing in flight stability. This is the same design theory that gives hollow point match bullets better accuracy properties.
In terminal performance, ballistic tips are designed to work like wedges, mashed into the hollow point and inside the jacket on impact, initiating expansion theoretically, quickly and reliably.