Dual citizenship is in general acquired at birth. For example you were born in America and your father was born in the United Kingdom and has hold a U.K. passport and was married to your mother when you were born. In this case you hold dual citizenship and you are entitled to apply for a U.K. passport even if you have never been in that country. However there are also cases that having two passports does not mean having dual citizenship. This applies to those countries which do not recognize dual citizenship. For example if you were born in India, have emigrated to the United States, have been naturalized in the U.S. and have gotten the U.S. passport you are supposed to turn back your Indian passport since you have lost your Indian citizenship..