In traditional classful IP addressing it was assumed that subnets would be contiguous. What that means is basically that to get from one subnet of some major network to any other subnet of that network, you would go through only subnets of that network. For example if you were in subnet 10.10.10.0 and you were going to 10.30.30.0 you might go through 10.20.20.0. That would be contiguous.
Discontiguous subnets means that to go from one subnet of a network to another subnet of that network you must go through subnets of a different network. For example if you are in subnet 10.10.10.0 and to get to 10.30.30.0 you must go through 172.16.10.0 then that would be discontiguous.
In traditional classful routing protocols (such as RIP and IGRP) discontiguous subnets are a problem. In more modern classless routing protocols such as OSPF discontiguous subnets are less of a problem.