The US is one of a small number of countries that taxes on the basis of citizenship, rather than residency. So all US citizens are required to file federal tax returns even if they live and work abroad full-time (as my brother does, in France). Because the US and France have a tax treaty which governs the payment of taxes by both countries' nationals, my brother's French tax payments are credited against the US tax he would otherwise owe on his income. So, he does not pay twice on his income.
In many other counties, the system is residency-based, not citizenship-based, so if you reside full time in a country where there is no (or lower) income tax, you are not liable to the country where you are a citizen for any tax on income earned outside of your home country. This is why you get what are called "tax exiles." (Ingmar Bergman is a famous Swedish tax exile, who lived abroad to avoid paying what he called was a 90% marginal tax rate.) Pat Rafter was an Australian tax exile who took advantage of the lower/non-existent tax rates on Bermuda. As a Bermuda resident, he only paid Australian taxes on income he earned in Australia, and not on income he earned in other countries. This would not be the case for US citizens, who would be liable for US taxes (some of which would get a credit) for all income earned both at home and abroad.
Yes, this will be on the test.