LAN - Local Area Network
When the devices are connected over a small area say a computer lab or an office building then that computer network is said to be a local area network or LAN. A LAN is generally owned, controlled and managed by a single person or organization. When required , a LAN can be set up in more than one building like an organization having multiple offices in the same neighborhood. In LAN, the users may or may not be connected to the Internet. If the requirement of the organization i sharing of resources( like printer )only then that LAN can be setup without Internet access.
WAN- Wide Area Network
When a network spans over a very large area like two different countries then that computer network is said to be a wide area network or WAN. The WAN is a collection of smaller LAN's which are dispersed geographically and are connected via a network device caller router. The Internet is the most common example of a WAN covering the entire planet. Mostly, WAN's are owned and managed by more than one organizations rather than a single one.
MAN - Metropolitan Area Network
When a network covers an area which is physically larger than a LAN but smaller than a WAN such as a city or a town the that network is known as a Metropolitan area network. It may be a single network such as a cable television network, or it may be a means of connecting a number of LANs into a larger network so that resources may be shared LAN-to-LAN as well as device-to-device. MAN's are generally managed and owned by a single organization which may be a local governing body or a large company.