1) In politics/sociology/history/ a colony is an administrative unit under the control of another geographically distant. Originally, as with the ancient (Hellenic) Greek apoikia, the term "colonization" referred to the foundation of a new city or settlement.
During the time of the Western (Europen and later Japanese) expansion (roughly 1400's - 1945), the term "colony" came to mean an overseas district with a native population, administered by a distant colonial government. Most non-European countries were colonies of Europe at one time or another.
The independence of these colonies began with that of the United States in 1776 and has continued until the present time, with for example Algeria and East Timor gaining independence from European powers only in 1962 and 1975 respectively.
2) In biology, a colony means several individual organisms of the same species living closely together, usually for mutual benefit, such as stronger defences, the ability to attack bigger prey etc. Some insects (ants, for example) live only in colonies.
Colonies were probably the first step towards multicellular organisms during evolution. The difference between a multicellular organism and a colony is that individual organisms from a colony can, if separated, survive on their own, while cells from a multicellular lifeform (e.g., liver cells) can not. Volvox is an example for the border between these two states.