To exchange means to trade one thing for another. If you and your friend both prefer what the other has brought for lunch, you should exchange lunches.
Exchange, which is both a noun and a verb, comes from the Latin ex-, meaning "out" and cambiare, for "change" or "substitute." If you're traveling in Europe, you exchange U.S. Dollars for Euros. If you get a really awful outfit for your birthday present, you can go to the store and exchange it for one you like better. The correspondence between you and your loved one is an exchange of love letters. An argument is an exchange of opinions.