The textbook definition of "administrative distance" is simple enough: "the measurement of a protocol's believability". It's not enough to know the definition, however you've got to know when AD comes into the picture and when it does not.
When a packet needs to be routed, the router looks in its routing table for the next-hop IP address the packet should take to get to the destination. There may be more than one matching path, in which case the router will look for the "longest match". The route that has the longest match - the route with the most bits in the mask set to "1" - will be the route that is used.
Consider the following three routes from a fictional Cisco router:
I 172.17.0.0 /24 via 172.1.1.1
O 172.17.0.0 /25 via 173.1.1.1
R 172.17.0.0 /26 via 174.1.1.1
This router has three possible next-hop IP addresses that it can send packets destined for the network 172.17.0.0. The masks are of different lengths, meaning that the route with the longest match (again, the route with the most bits set to "1") will be used. In this example, the RIP route will be used, since it has the longest match with a mask of /26. The administrative distances do not matter.
AD does matter when the masks are the same length, as shown here:
I 172.17.0.0 /24 via 172.1.1.1
O 172.17.0.0 /24 via 173.1.1.1
R 172.17.0.0 /24 via 174.1.1.1
The longest match rule always precedes the use of AD, but here there is a three-way tie regarding the masks. They're all /24 (or 255.255.255.0 in dotted decimal). AD will be used to break this - continued below ...
