I have been offered "exchanges" for an article in a very small publication in my vacation town, that does not have the budget to pay for articles. What does that mean?
I'm guessing it means they will give you printed copies of their publication in exchange for your article. You could keep one copy in your portfolio, and distribute the other copies to agents or editors (to show that you're a published author).
Or, it means they will give you advertising space in exchange for your article, which you could use yourself or sell to someone else.