A Contiguous network is a single Class A, B, or C network for which all routes to subnets of that network pass through only other subnets of that same single network.
A discontiguous network will have two or more subnetworks of a classful network connected together by different classful networks.
Discontiguous subnets are really a major issue when it comes to classful routing protocols or trying to achive intelligent summarization across your network. Otherwise, most major routing protocols can adapt to them - it just results in a larger routing table.
Say you have 10.8.0.0/16, 10.9.0.0/16, 10.10.0.0/16, and 10.11.0.0/16. If you own all of these networks, you could advertise them summarized as 10.8.0.0/14.
However, if you only owned the 10.8, 10.9, and 10.11 network spaces, you could not. You would then only be able to summarize it down to two routes - 10.8.0.0/15, and 10.11.0.0/16.
The idea is that contiguous subnets can all be reach in the same direction. So if you have 4 routers, and routers A, B and C all point packets destined to 10.8 through 10.11 to router D via a summary address, that works so long as the 10.8.0.0/14 network all resides off of router D. However, as explained earlier, if 10.10.0.0/16 resides on router B, then traffic destined to that network would not reach it's destination. That is a case where you break up your summarization as the networks are no longer "contiguous".
You can search Cisco.com for the words contiguous and discontiguous and you will find some articles that provide graphics and slightly better explanations.
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