Dual citizenship doesn't exist. It's a slang word for someone who is a citizen of two countries. Triple citizenship is having citizenship in three countries, and so on with quadruple, quintruple, etc. All this is covered under "multiple citizenship."
Somebody who is a citizen of two countries has more rights and more responsibilities than someone who is only a citizen of one country. Let's say someone is a citizen of the Netherlands and the United States. As such, he's not allowed to smoke pot in the Netherlands like his fellow nationals, as it violates US law, and he also can't travel to Cuba as that violates US law as well. A citizen of two countries is always a citizen of two countries and as such he always has to obey by the laws of his two countries of citizenship.
In contrast, the advantage is that such a person has more choices on where to live. In the aforementioned example, he could live in all of the European Union and the United States including Puerto Rico, the US Virgin Islands, Guam, and American Samoa. So if the sh*t ever hits the fan in one part of the world, he can simply pack his bags and move to the other part.
An immigrant from Europe, I now live on the American Rivera and work as an attorney in Santa Barbara, California.