Concept under which a person can be a citizen of two different countries. This can be by birth in one country to a national of another (in countries which confer citizenship ius solis), by birth to parents of different nationalities (ius sanguinis on both sides) or by acquiring citizenship in a second country by virtue of fulfilling residency or other requirements.
Some states require that their citizens be only citizens of that country, to the exclusion of all others, and forbid the acquisition of citizenship of a second state on penalty of withdrawing the original citizenship. The United States is technically one of those countries though I've heard no reports of it ever happening. Naturalised citizens of the United States are obliged to renounce the citizenship of their country of origin but the authorities very rarely check.
In some cases, dual citizenship may be unavoidable despite laws to the contrary if the person is born to citizens of two countries whose laws automatically confer citizenship to children born to their nationals and have no provisions for renouncing or revoking it. Many countries, the US included, legally accept and allow this.
Dual citizenship is otherwise irrelevant to the country the person is living in. If s/he lives in a country of which s/he is a citizen, the second one is ignored. If in a third country, they are treated as a citizen of the country whose travel document they entered with, though they could probably request consular assistance from either.
Yes, I hold dual citizenship.