The concept of ethnic origin is an attempt to classify people, not according to their current nationality, but according to commonalities in their social background. For example, somebody living in a monocultural environment, speaking English for example and clearly a member of an English-speaking cultural milieu, may be descended from immigrants speaking some other language and still participate in some other aspects of their culture.
Ethnic origin implies one or more of the following:
Ethnic origin has become a popular classification in statistics, where the concept of races has been largely discarded since World War II, for various reasons. A reaction against the abuses of the Nazis and apartheid made it hard to collect, store or publish racial data. Social scientists in general have lost interest in race as useful concept of study, with many other differences between population groups more significant. However the relative prosperity of distinguishable groups remain of interest in public policy discussions.
In the US, however, the use of the term race is still current. The census asks questions about race, though the classification used is no different from what would be termed ethnic origin elsewhere.
The concept of ethnic origin in practice may seem arbitrary and without a rigorous definition of how to assign a person to the particular categories. If a person was asked for their ethnic origin and answered "how do I tell what ethnic origin I am?" it may not be clear whether they are being asked for: their country of birth, the country of birth of their parents, or more distant ancestors (how distant?), or for a description of their appearance, such as skin colour or hair type, or for their cultural behaviour such as food, clothing, language and the people they associate with. The answers to these questions may be contradictory and suggest different ethnic origins.
The answer of interest to the questioner is probably whether the person considers themselves to be a member of a particular ethnic subdivision of society, or are considered a member of such a group by others. This would affect whether they were possibly subject to discrimination etc. However the question is still open to interpretation, since a person may be identified differently depending on the mode of contact, e.g., considering outward appearance such as skin colour or clothing, name, or use of written or oral language, etc. This raises the question of whether ethnic origin is just another term for ethnic group.