The Class A, B & C address model worked fine in the early years
of the Internet. Towards the end of the 1980s and in the early 90s
it became increasingly clear, with the observed exponential growth
in the number of Internet hosts, that it would soon "break" under
the load.
The main problems were observed to be:
Internet routing is done on the basis of the network part of
the IP address. Major backbone routers were stuggling to maintain
routing tables which included information about how to send a
datagram to all of the allocated networks -- the amount of routing
table memory required was becoming impractical.
Addresses themselves were running out. The inflexibility of the
network class-based system meant that many organisations were being
allocated class-B networks, when their requirements were not far in
excess of the capacity of a class-C. The end result was that vast
slabs of the address space were never allocated, and effectively
wasted.
A (temporary) solution to both of these problems was introduced by
the IETF in 1993 -- Classless Internet Domain
Routing, or CIDR (pronounced like
"cider"). In this system, the entire class A, B and C scheme has
been discarded for all recent IP address allocations.