Colonialism means the rule of one country over another country. The people of the ruling country stay in their own homes. But the imports from the colonized country (or the country ruled by the colonial power) make them rich.
European colonialism started in South Asia when Vasco de Gama arrived at Calicut. The Dutch, the French and the British also followed them soon. They arrived here at first as traders, but trade in those days was dangerous business because the merchants were required their own guards (the police did not protect the merchants). The European also obtained permission from local rulers to keep small private armies. Later they use these armies to fight each other and also to gain control of the native states. At the end, the British took control of almost all the south Asia and the other European powers had to leave.
There were two main reasons why the Europeans gained control of South Asia so easily. First of all, they have superior weapons and better military techniques. This proved to be great advantage to them in wars against the local rulers. Secondly, the Europeans had better understanding of politics due to liberal education in their own countries. By 1805, almost the whole South Asia came under the control of the British East India Company, and later the British government took over after the war of independence (or the Mutiny) in 1857.