A classful network is a network that is based on the default class A, B or C networks. Classes A, B and C are defined as follows;
Class A: 0 – 126 with a mask of 255.0.0.0 (/8)
Class B: 128 – 191 with a mask of 255.255.0.0 (/16)
Class C: 192 – 223 with a mask of 255.255.255.0 (/24)
If you are using a routing protocol that supports only classful networks (such as RIP v1 and IGRP) then all devices in the same network must use the same subnet mask. Since routers running a classful routing protocol do not include subnet mask information with routing updates, the router assumes either its own subnet mask, or defaults to the classful subnet mask.
A classless network, allows the use of variable length subnet masks, or VLSM as its known, because subnet mask information is included with routing updates. You can have a mixture of different subnet masks in the same network, eg
Classless IP addressing means you can use any subnetmask you want, even assigning partial blocks.