Colonization is the act of one country settling another place, in order to become the new rulers of the new country, and to live in the new country. An early example is the settlers who went from the cities of Ancient Greece to start new cities.
In 1492, Christopher Columbus landed in The Americas. This is how the Europeans learned that North America and South America were there. The Europeans colonized the Americas. Because of this, and the killing of many Native Americans, most people now living in North America are the descendents of Europeans.
Sometimes, science fiction stories talk about space colonization on space stations or planets other than Earth. Some science fiction stories like The Matrix speak of the robots the human beings made, taking over, and colonizing Earth.