Any number of factual situations can bring an international element into a separation or divorce matter. There might be assets located in two or more countries. The spouses may have been born in, or be citizens of, two different countries. It could also be that the spouses reside in two (or more) different countries, or have jobs that bring them to different countries. Or one parent may wish to move with the children to a different country.
Basically, if one or both of the spouses have some connection to a different country, then their divorce can be called international.
An international divorce is different because the laws of two or more different countries might apply, and cases might be filed in the courts of multiple countries. In addition, differences in cultural expectations, language, currency, or even time zones can have an effect on how the divorce is handled.
Obviously, this makes an international divorce more complex and difficult than a purely domestic divorce. More options, decisions, potential traps and pitfalls exist in the international context.
This is why getting early advice from an attorney with experience in international divorce issues is important. It might even be wise to get input from lawyers in the other country or countries involved. The main thing is to recognize when a separation or divorce situation has international elements, and to get the right advice as soon as possible.