Their president, Yanukovych is from the Russian minority in the Ukraine (70 Ukrainian / 30% Russian) who mainly live in the eastern-industrial region around Donetsk, which is his power base. West Ukraine is much more European looking whereas the east looks more to Russia.
What he has done is painted himself into a corner by going so far down the road on talks for the the EU EEA agreement which a majority want, but he has mismanaged the Russian situation where they are playing hardball, with selective import bans for 'technical and safety' reasons where they want Ukraine back under their sphere of influence and ideally part of their customs union, which is not compatible with the EU EEA agreement.
Where 50% of Ukraine's exports go to Russia and most of the rest to Western Europe he has no choice but to try and buy himself sometime. The only way he can do that is by coming to some sort of agreement with Russia, but if he tries to join the customs union he will be committing political suicide or worse and will have no chance of being reelected in 2015. If he signed the EU EEA agreement and Russia bans their exports then Ukraine is toast financially. So I think he will try to sit on the fence and muddle through by offering the EU EEA agreement in the future but saying financially they cannot afford to sign it now and do some sort of short term deal with Russia. He will then hope to get more financial support in the form of loans from the EU, and then probably sign just before the presidential elections in 2015 as he will need this to stand any chance of reelection. If he can delay it until the presidential nominations have closed before releasing Yulia Tymoshenko that would suit his purpose and reelection hopes just fine.
He has made a big mistake, jilting a bride at the altar, is guaranteed to really annoy the brides family as he has found out. Where is is now sat on a fence who knows how many splinters he will collect from each side.
The real political struggle is about modernising the country, fighting corruption, and vested interests, that holds so many people back, so Ukraine becomes a modern richer democracy, with the the average Ukrainian better off. Many Ukrainians still live under the UN poverty level of having less than $1.5 per day to live on. The minimum wage is about £75 a month, if you have a job, so if a family has to survive on this you can see the poverty issue.
The Ukrainian population is very well educated, being the 4th best in the world, but vested interests, a legacy of soviet rule and widespread corruption make it very difficult to get ahead.
After the privations the Ukrainians suffered under Soviet rule, especially in west-Ukraine these have not been forgiven or forgotten as the crowd in Kiev have shown. West Ukraine is the old power base and area where the Cossacks originated from and the people are as hard as nails.