To decolonize is to stop ruling over a territory and allow it to be independent. The main goal of the American Revolutionary War was to get the British to decolonize the territory later known as the United States.
Before the Revolutionary War, the future U.S. was composed of thirteen British colonies. When a colony breaks away from the colonial empire that controls it (or if the empire itself breaks apart), it decolonizes. This verb is also increasingly used for the process of reclaiming a culture that's been lost while under the control of another country. When indigenous people decolonize, they often relearn native languages and redefine themselves as part of their traditional community.