According to the BBC, they are protesting the Ukrainian government’s rejection of a treaty to join the European Union.
What the protestors are trying to stop is the handing over of the Ukraine to Russia. Joining the EU was considered by many Ukrainians to be insurance against any future Moscow take over of Ukraine. Now those Ukrainians believe they will see their country - under its current leadership - slowly put their homeland into a Russian orbit of control. Back to the bad old days in other words.
Things have been heading on this direction for years: http://news.bbc.co.uk/2/hi/europe/8503177.stm
Everybody there knows what is really going on:
And guess who the pro-Moscow party is most party is most worried about? http://www.news.va/en/news/major-archbishop-sviatoslav-ugcc-will-remain-faith