Etymologically, traceable back to about the 12th Century, Krajina (whence Ukraine or Ukrayina) meant "borderlands" or "frontier." In the time of the USSR, and even before, Ukraine was considered a frontier, and hence called "the Ukraine," much the same way the Dutch word nederland gave us "the Netherlands."
After gaining independence from Russia, Ukrainians decided that despite the etymological venerability of their name, to be called anyone else's frontier was demeaning. Hence, they kept the historical name but dropped the definite article in English renderings. Officially, the name changed from Ukrainian Soviet Socialist Republic to simply Ukraine, but this didn't stop common usage from referring to them as the Ukraine any more than the former name made their political system a republic. Ukrainians are somewhat sensitive about their country being called "the Ukraine" by Westerners, since it doesn't recognize their sovereignty and implies they are still just a frontier of Russia.
This information comes from what Ukrainians themselves told me when I was visiting Kyiv (called Kiev by Westerners) in 2004. Since then, I've also noticed a shift from na to v' for referring to being in Ukraine. One is on (na) a mountaintop while hiking, or at (na) a ranch while working with cattle. Back when Ukraine was the Ukraine, Ukrainians and others said they were in (na) Ukraine while in-country. Now they say one is in (v') Ukraine. V', like most prepositions, has multiple translations, but most properly means in or of. This was the preposition Ukrainians themselves used when traveling -- I'm in (v') Russia today, or in (v') France. Yet until very recently, they were only ever in (na) Ukraine, even when speaking of themselves at home. To me, this means that the etymological underpinnings of Krajina have only recently been subsumed by politics. A case could be made for saying the linguistic change implies that those in Ukraine considered themselves to be on (na) the frontier until very recently.
Of course it's all politics now. Sensitive Westerners don't use the definite article.