To colonize is to settle in, and take control of, land outside your own borders. Usually, a large, powerful country colonizes a territory or area that's much less powerful.
There are many examples through history of powerful countries that colonized various regions of the world in order to gain natural resources or to obtain more land for their citizens to live in. When this happens, it's rarely good news for the people who lived there already. Colonize and colony come from the Latin colonus, "tenant farmer" or "settler in new land," from the root colere, "to cultivate, till, or inhabit."