Compared to Cat5 cables, Cat6 cables have stricter performance specifications and allow for higher data transfer speeds than Cat5 cables. They're manufactured to be more durable and tightly wound, which helps protect their parts from damages that cause data transmission problems you'll often see in Cat5 cables.
However, if your Internet plan speed with your ISP isn't close to, over, or at 1 Gbps, you won't really benefit from using a Cat6 cable instead of the cable type usually provided by ISPs, a Cat5.