Citrus fruits grow well in South America. One reason that they are a natural product for trade is that they are sweet, and as post #4 mentions they also provide health benefits, especially for sailors who were susceptible to scurvy. They would take them with them, and people at home would be exposed to them.
One famous use for citrus fruits in the Atlantic economy was to avoid scurvy, the vitamin-C deficiency which plagued not just sailors, but many others in colonial societies. As others in this thread have said, citrus fruits originated in the Old World, and came to the New World with settlers. Many, however, were mass-cultivated for the first time in the New World. The grapefruit would be one example of these.
Citrus fruits seem to have been introduced from the old world into the new. Various reasons probably explain their introduction, including the idea of cultivating them in climates that were often very hospitable, and also the idea of providing people from the old world with foods with which they were already familiar and which they had come to enjoy.
I don't quite understand. The Columbian Exchange wasn't a process where things were used for anything. It was just that some things got brought (on purpose or not) from the Old World to the New and others were brought the other way.
Citrus was brought by the Europeans to the Americas. It was brought for food and because it helped protect sailors from scurvy. Is that what you're asking?