Eastern Ukraine is highly industrialized and populated in majority by ethnic Russians. They have closer ties to Russia and generally support the "return to center" that has allowed Putin to put Russia back on a "Soviet footing." The majority in the current government is drawn from the eastern Ukrainian population and favors stronger ties (and possibly some sort of political consolidation) with Russia.
Western Ukraine is highly agricultural and populated in majority by ethnic Ukrainians. The minority in the current government is drawn from the western Ukrainian population. They have much closer ties with Eastern and Western Europe and want Ukraine to distance itself from Russia to become part of the European Union.
The history behind the East/West divide dates back to Czarist times. When oil, coal, and strategic minerals were discovered in eastern Ukraine, the Czar began relocating ethnic Russians to work them. This practice continued after the Revolution and picked up steam under Stalin and especially Khruschev. It divided the nation in two, and made many ethnic Ukrainians second-class citizens in their own country. During the Second World War, many western Ukrainians sided with the Nazis and fought a guerrilla campaign against the Soviet military not because they believed in Nazi ideals, but because they felt it was their best chance to regain control of their historical nation. After the war, Stalin's vengeance was swift, merciless, and indiscriminate and the population of western Ukraine (literally) decimated. This furthered to deepen the divide. Ukraine's bid for independence in 1991 was led by western Ukrainians but supported by the youth of eastern Ukraine, and so was successful. As those youth aged and lost their idealism, they fell back into their parent's ideology and the cycle began again.