In a typical LAN (Local Area Network) a group of computers and devices are connected together by a switch, or stack of switches, using a private addressing scheme as defined by the TCP/IP protocol.
Private addresses are unique in relation to other computers on the local network. Routers are found at the boundary of a LAN, connecting them to the larger WAN.
In a WAN (Wide Area Network) you will have multiple LANs connected together using routers. I was taught many years ago that a WAN had nothing to do with the size of a computer network, but was simply connecting multiple LANs together across the public highway system, such as the internet.
If you have a three computer LAN than uses the public highway, as in the internet and internet addressing, to connect to another three computer network, the two LANs working together form a WAN.
People often try to explain concepts like LAN and WAN using terms and descriptions that have nothing to do with the definition. I often see people put numbers of computers into their definitions of LAN and WAN. The number of computers is not significant to the definition. The physical type of connection, as in copper wires, fiber, wireless, has nothing to do with the definition.
You may not be familiar with the specific function of a network switch versus a router, or the definitions of private addressing scheme versus a public address, they are more advanced topics of computer networking, but they are the core elements that separate a LAN from a WAN.
The all encompassing footnote
I realize that I may have oversimplified some terms, but my goal was to deliver a basic understanding of the concepts of a LAN versus WAN without delivering a lecture on computer networking fundamentals. IMHO, many answers given to simple questions on online forums over complicate matters as well as add quite a bit of stray information. A LAN could use something other than a TCP/IP addressing scheme, but the illustration of a LAN and WAN based network as I describe is a typical implementation.
These definitions were written off of the top of my head based on many years of networking experience. Any resemblance to Wiki or any other website is merely coincidental. (Since I am defining basic terms I would hope that they are at least similar!) I used the task of answering some basic computer networking definitions here on Quora as inspiration to update my very neglected website on computer networking.
See more at: