Wikipedia definition 

Micronations, sometimes also referred to as model countries and new country projects, are entities that claim to be independent nations or states but which are not recognized by world governments or major international organizations.

Micronations are also distinguished from imaginary countries and from other kinds of social groups (such as eco-villages, campuses, tribes, clans, sects, and residential community associations) by expressing a formal and persistent, even if unrecognized, claim of sovereignty over some physical territory.
Several micronations have issued coins, flags, postage stamps, passports, medals, and other items, which are rarely accepted outside of their own community.
The earliest known micronations date from the beginning of the 19th century. The advent of the Internet provided the means for people to create many new micronations, whose members are scattered all over the world and interact mostly by electronic means, often calling their nations Nomadic Countries. The differences between such Internet micronations, other kinds of social networking groups, and role playing games are often hard to define.
The term "micronation" to describe those entities dates at least to the 1970s.[1] The term micropatrology is sometimes used to describe the study of both micronations and microstates by micronationalists, some of whom refer to sovereign nation-states as "macronations".

Here are a few Micronations :)

Aerican Empire Founded 1987, Population 260
Territory includes a colony on Mars & northern hemisphere of Pluto. Citizens worship the Giant Penguin.

Dominion of Melchizedek, Founded 1990, Population 100
Ecclesiastical state claiming rulership over the Earth. Also a tax haven with 300 banks & linked to white-collar fraud.

Principality of Seborga, Founded 1963, Population 350.Small villae where the population elects a monarch. Has it's own currency, stamps & genuine independence movement.

Principality of Hutt River, Founded 1970, Population 20. Established by a disgruntled farmer.Residents are exempt from Australian income tax.

Conch Republic, Founded 1982, Population 25000.Spoof state created as a protest by Florida Keys residents.Successfully saw off a planned US invasion in 1995.

Freetown Christiania, Founded 1971, Population 850, A hippy zone made famous for it's thriving hash market. Won the legal right to run its own affairs in 2011.

Republic of Molossia, Founded 1999, Population 27, Set up in Kevin Baugh's backyard.Has a space program that launches toy rocket ships.

Grand Duchy of Westarctica, Founded 2001, Population n/a. No country has ever laid claim to Marie Byrd Land in Antarctica.Travis McHenry took it for himself.

Republic of Minerva, Founded 1972, Conquered 1972, Attempt to create a utopia on an artificial island.The government of Tonga invaded & annexed it.

Principality of Sealand, Founded 1967, Population 27, Built on an anti-aircraft platform lying just outside of UK jurisdiction. It's rulers have fought off mercenaries to maintain control. Have there own stamps etc..