Trans-Dniester is a
breakaway region from the post-Soviet republic of
Moldova. It is a thin strip along the north-east bank of the River
Dniester, and is predominantly Russian-speaking, whereas Moldova is mainly Romanian-speaking.
Historically it was a Russian territory used as a stalking-horse for their ambitions on Romania. After the formation of the Soviet Union, a small republic of Moldavia was formed within Ukraine, by its border with Romania, in 1924. This is essentially the Trans-Dniester republic of today.
Romania is based on two old principalities, Moldavia and Wallachia. The first Soviet republic of Moldavia was not part of historic Romanian Moldavia, and did not have a Romanian-speaking majority. These principalities had long been vassals of the Ottoman Empire, but in 1812 Russia acquired half of Moldavia, the region called Bessarabia.
Later in the nineteenth century Romania broke free of the Ottomans. With the fall of Tsarist Russia, Bessarabia was ceded to Romania in 1918.
In 1940 the Soviet Union advanced on Romania and annexed Bessarabia once more, and attached it to their own previously artificial Moldavia. (Romania, a Nazi ally, retook it in 1941 but was again displaced in 1944 as the Axis was driven back.) The resultant Moldavian S.S.R. was now a majority Romanian-speaking territory within the Soviet Union. It was this that gained independence as the Republic of Moldova on independence in 1991. (Moldova is the Romanian form of the name, traditionally Moldavia in English.)
The Russian inhabitants, now a minority within a republic that at first seemed bent on reunification with Romania, got shirty and declared their own republic. Violence followed and Russian troops are keeping the peace there. There is some nominal adherence in some quarters to the idea of autonomy within Moldova, now that Moldova has renounced all ambition to unite with Romania, but the region is effectively independent. There is another ethnic minority region in Moldova, that of the Turkish-speaking Gagauz; they now have a comfortable autonomy.
The river it's across is called the Dniestr in Russian, the Nistru in Romanian. In English, either Dniester or Dniestr. The region is called Pridnestrov'e in Russian, Transnistria in Romanian. In English you see Transdniestr, Transdniestria, Dniestr, and such like. The official English-language designation of the secessionist state is the Trans-Dniester Moldavian Republic.
Independent Moldova introduced a flag based on Romania's, with a coat of arms for differentiation. Trans-Dniester continued to use the Soviet Moldavian flag at first, a quarter-width green horizontal stripe on red, with the gold hammer and sickle; but they later changed to simple red-green-red. However on 25 January 2000 the hammer and sickle was once more officially placed on the state flag.
The capital of Trans-Dniester is Tiraspol. The current president is Igor Smirnov. They have their own currency, the Trans-Dniester rouble.