The US requires US citizens to file a return for federal and state income taxes. Interestingly, per the 2017 IRS guide, page 5, it does not matter whether the US citizen resides in the US, or whether the income derives from US sources.
Thus, a US citizen residing outside the US and drawing income entirely from non-US sources would still be required to file for US taxes. In principle, this would even apply to US citizens that were born abroad and never set foot in the US.
This seems to be very uncommon in the rest of the world. For instance, on Expats.SE, it is claimed that only the US and Eritrea tax non-resident citizens on foreign income, and when I as a German national lived and worked in Switzerland, Germany didn't care about my Swiss income. (The Swiss did care about my German income, though.)
I assume that following up on foreign income on non-resident citizens is a big hassle for the IRS. Plus, people qualify for the Foreign Tax Credit and Foreign Earned Income Exclusion, so whatever the IRS does collect in such cases is further reduced. It seems to me like the taxes collected in this manner will likely be trivial compared to any serious enforcement costs. (I would welcome any statistics proving me wrong, or backing this up.)
What is different in the US from the rest of the world to cause this? Has there ever been a political discussion, say in Congress, in which someone explicitly articulated a reason why this practice should continue? I could imagine a couple such reasons, e.g., that US citizens will be eligible for consular protection no matter where they live, and so they should darn well pay for it - but that would apply to citizens of other countries, as well, so it doesn't really tell why the US took a different view of this matter than everyone else.