A routable IP address is one that can be reached (or routed) by anyone on the internet. You need this so that when you type www.yahoo.com, they can send you the information.
A non routable IP address means internet people can't reach you. (inTRAnet people can.) My computer has a non routable IP address of 192.168.0.101. My router takes the IP address my ISP give me, and assigns non routable address for the computers on my network. This makes it much harder for people to try to hack my computer. (a router is harder to hack then windows...)
Hopefully this answers your question, edit your post if you need more info.
Edit: To add to what Jombi said, there is one other important IP address, which is technically a non routable address. (its more properly called a reserved number.) 127.0.0.1 is the local machine's address. Technically every computer has two IP address's, the routable/non routable that is assigned to it by some other device, and 127.0.0.1.