Many people have “offshore” accounts, including anyone who spends time in both Eretz Yisrael and Golus, since a bank account in one is an offshore account in another. For Americans, this requires filing one simple tax form per year.
The term “offshore” means “not in your home country”, and isn’t a big deal UNLESS you are doing in secretly (usually to avoid taxes, sometimes to avoid the local equivalent of the “Shin Bet”, the “FBI” or the KGB)