An exchange student
is a student (almost always of high school age) who temporarily goes abroad and lives to live with a host family in a foreign country, and attend school there. That host family often also sends a child of theirs abroad, usually to the same country as the student they are hosting. In this way, the two students are said to have been "exchanged," essentially temporarily trading countries with each other.
The main purpose of exchange programs is to increase cultural understanding, both for the student and the people in the host country he/she comes into contact with.