Here's the situation in brief: Russia and the outgoing Ukrainian President support PM Viktor Yanukovich, the outgoing PM's handpicked Russia-leaning successor to become the new Ukrainian PM. His rival is Viktor Yushchenko, a Western-leaning reform-minded former PM who was ousted by a coordinated effort of the business oligarchs who benefitted from state-sponsored contracts in the immediate post-Communist years and who pull the marionette strings of Ukrainian politics. The Presidential election was two-pronged: first an election among numerous candidates, then a run-off with the top two (this is how the French presidency is decided). The losers in the first round threw their support to Yushchenko. Exit polls after the elections (which are reputedly very accurate, according to WSJ's David Satter) indicated a 54-43 edge for Yushchenko; the vote tally was 49-46 for Yanukovich.
The problems with the election, the fact that the state-run media (all but one TV outlet in Ukraine is state-controlled) was used as part of Yanukovich's personal campaign (Yushchenko had virtually no air time, there were no debates, etc.), the incredible fraud in the eastern 1/3 of Ukraine where Russian influence is strongest and the detailed allegations of vote fraud uncovered by Yushchenko and international monitors (even Jimmy Carter won't certify this election!) are extensive and too detailed to relate here (go here for some links to background info). Yushchenko supporters have swamped Independence Square in Kiev and held 24-hour vigils protesting the results since shortly after they were announced (and its COLD in Kiev; plus the Yushchenko supporters have been ordered to stay sober -- no vodka, in a country where the distilled hooch is a birthright). Vaclav Havel wrote to Yushchenko to give support, Margaret Thatcher has registered her support for Yushchenko and his supporters and Lech Walesa has appeared in Kiev to support Yushchenko.
International pressure (the US has refused to recognize Yanukovich's "victory," as has the EU), internal pressure and the overwhelming evidence of fraud have now combined to force Yanukovich to offer Yushchenko the post of PM if the latter would call off the protests; Yushchenko refused. See here for an update on the momentum building for a new election either nationwide or in the highly corrupted eastern Ukrainian provinces where the dead supposedly voted early and often.
Why is all this important? Ukraine is (mostly) seeking to join its western neighbors Poland, Slovakia and Hungary in establishing a democratic system that is fair and open, Western-leaning, untainted by former Russian dominance and stripped of the USSR's legacy. Because it borders Russia, and has a large ethnic Russian population, Ukraine's transformation process is basically 10-15 years behind Poland's and Hungary's. Plus, Vladimir Putin has made no secret of his desire to rebuild a sphere of influence centered in Moscow and comprising the former Soviet states, such as Georgia, Chechnya, Ukraine, Byelorussia, Uzbekistan, etc. In other words, this is Putin's power play for establishing a benign dictatorship and preventing democracy from germinating on his southwestern border. (See here for Putin's reaction to the foreign pressure on Ukraine; Putin has TWICE recognized the election result -- Russia is the only major foreign government to do so). Thus, as John O'Sullivan notes, there is more than just that country's presidency at stake in Ukraine.
Click the link in the title for more. Note that this is Pres. Bush's opportunity to help guide a sizeable country and ally on its road to democracy. His father did this reluctantly in the 1989-91 period as the USSR crumbled; the current Pres. Bush should take the reins more firmly and establish that free and fair elections, transparency in politics and an independent media not used as a state tool are of paramount importance as the US seeks to spread liberty throughout the world.
HT: El Capitan. See also here for why the US press narrative (east Ukraine/west Ukraine, "disputed" results v. flat-out fraud) is wrong.