Lets say you own a company that has 5 different locations in town. You are a small local chain. Each store has it's very own LAN, which is local to the computers in that store. All access from computer to computer in the same building will be over the LAN. Now, each building has their own separate LAN. When a computer talks to another computer across the buildings they are traveling over the WAN network. Each of them are still connected, buildings 1 through 5, but they are so over a WAN. So, if I am in building 2 and need a file off of a computer in building 5, I would have to travel over the WAN to get to that file.
Typically WAN traffic is a lot slower than LAN. So, a lot of network admins will set up replica servers at each site and they will replicate down from the master server in the central office. This reduces a lot of WAN traffic and keeps it on the local network.