CIDR

CIDR stands for Classless Independent Domain Routing. It replaced Classes A, B, C networks on the Internet. The CIDR notation counts how many left-most bits are contained in a netmask. So that a class A would be a /8, a class B would be a /16 and a class C would be a /24. A /32 is an individual IP and /0 represents the entire Internet often used with firewalling.

IPv6
An IPv6 CIDR notation is natural because you have a prefix and a prefix length. If the prefix is fd00:f00:: and the prefix length is 64 then the notation would be fd00:f00::/64 or similar.