There are three main classes of IP addresses. You know about A, B, and C already, right? If not, you are lost already; this is not the post for you. You need to gain an understanding of IP addresses before you venture further. It is painfully boring, but it is information you will use on a daily basis in the networking world. Just Google or Wiki "IP addressing and subnetting".
Your Cisco router is classfull by default. This means that it will obey the conventions of the IP classes when routing. If you have configured RIP as your routing protocol and enabled the network 172.16.0.0 for broadcasts, then your router will assume that the interface with an address on 172.16.0.0 will be able to route all 172.16.0.0 traffic.
Here is the problem: Let's say that Fastethernet 0/0 on your router is at 172.16.1.1 with a 255.255.255.0 address. This means that it is attached to a network that includes 172.16.1.1 through 172.16.1.255, right?
Now, your router is also attached to a 10.10.10.0 network, which attaches to a remote router with an interface in the 172.16.99.0 network (/24 or 255.255.255.0 subnet mask, as well.) Therefore, the remote router (which shares RIP updates with your router) can get to 172.16.99.1 through 172.16.99.255 and your local router knows this; you can see it in the routing table.
The point of using RIP is so that your router and the remote router talk to each other and share this information, right? So, if your local router receives a packet destined for 172.16.99.100 it should look in its routing table and see that the most specific match is to use the 10.10.10.0 network and route the packet to the remote router, which has a directly connected interface in the 172.16.99.0 network. However, if you have left the router defaulted to "classfull", this will not happen.
If your router is operating as classfull, it will take a packet destined for 172.16.99.100 and only look at the "172.16" portion. That is bacause those are the only octets relevant in a class B address. If it is only looking at the first two octets when it makes its routing decision, the router will choose the directly connected interface with "172.16" every time--even though that interface does not have access to 172.16.99.100. Stupid router.
If you want to make your router a free spirit, throw out the conventions of classfull routing, break all the rules, and find its way to 172.16.99.100, you need to enter the following command:
Router(config)#ip classless
Your router will no longer have any class, just like you. More importantly, your router will look for a more specific match in its routing table, taking into account the subnets that it knows about through RIP.