This is my rough understanding of what's going on:

Ukraine wants to increase cooperation with Europe, and possibly join EU. This would undermine it's relationship with Russia.

The previous Ukranian president, Viktor Yushchenko, usually sided with the West, and current president, Viktor Yanukovych, wants to preserve friendship with Russia.

Russia obviously doesn't want to lose allies, so it threatened to stop trading, and impose strict sanctions on Ukraine if they agreed to partnership with Europe.

Some Ukrainians dislike Yanukovych for siding with Russia instead of Europe, thus causing protests.

If you have more knowledge about this situation, feel free to correct me if I err.