Colonialism
Colonialism is the expansion of a nation's sovereignty beyond its borders through the establishment of colonies. It is usually seen as a substantial part of imperialism, especially when involving sovereignty over foreign cultures or peoples.
Colonialism typically involves the spread of a nation or people's culture through the establishment of new settlements (eg. English settlement of the New England states or opulation transfers to existing settlements (eg. Dutch dominance of South Africa.)
Colonialism is most associated with the Roman Empire, British Empire, and French control of Africa.
Misuse of the Term
Anti-Americans and liberals in general commonly deride American foreign policy as colonial or imperial, which is deceitful, as the United States has no colonies (having relinquished the Philippines, which had previously been Spanish, not sovereign), made Hawaii a state, smaller lands (Guam, etc...) protectorates, and purchased or legally acquired other territories (Guantanamo, Panama Canal).