Before the introduction of CIDR, IP addressing was based on a classful network system, where Class A, B, and C networks were defined by the first few bits of the IP address. Class C networks, identifiable by the first three bits being '110', were designed for small organizations and could support up to 254 hosts. This system, while simple to understand, led to inefficient use of IP address space and contributed to the rapid exhaustion of available IPv4 addresses.