Erasmus is a common word in european language, meaning "exchange". Imagine you live in Paris, you're a French person, you will probably "go on an erasmus" during your studies. You will study abroad during one semester, in Berlin for example.

In Europe, we also say "erasmus" for people who went abroad, outside the EU (USA for example). It's harder to go on an exchange in the USA as you have to translate your grades, everything is more expensive (no european health insurance, etc).

Hope this helps.