What Is a LAN
A LAN is a Local Area Network. This is a network which exists in one specific location, and is relatively small. You can think of a LAN like you think of the internal phone system of an office. Every employee has an extension, but it is only an internal extension -- it is not a "real" phone line which is connected only to his own phone. To call from one extension within the office to another extension, you only have to dial two or three digits -- it is an "internal" call. It does not go through the public telephone system, and it will actually work even if the office has no external phone lines at all.
This is exactly the same also for a LAN. To get from one computer on a LAN to another computer on the same LAN, you do not have to go through any other network. It is a private network.
Below, you can see what is a LAN, in relation to a WAN (as previously explained):
There are certain types of communication which are unique to a LAN. One such type is called 'broadcast' communication. This is where one node (station, host, computer) on the LAN 'shouts out' so that all other nodes hear the message. This is similar to pressing the 'announcement' button on an office telephone, and using all the phones connected to the system to broadcast a message to all employees (through the speaker of the phone).
Naturally, such a feature would not be practical with the national telephone system. The system would simply collapse. The same is true for broadcast requests in a computer network -- they work only on a LAN, and will not go out to the whole WAN.