The term "Eastern Europe" is ambiguous, and there is no consensus as to what constitutes "Eastern Europe" in a historical context. There is no mountain range or other geographical feature that neatly divides Europe into east and west. Cultural divides are even more problematic. Do you base it on ethnicity? If so, do the Western Slavs count as Easterners or Westerners, since they embraced Catholicism, the Latin alphabet, and other Western cultural norms? And do we allow for the boundaries or Eastern Europe to shift with time? After all, the dispersion of ethnicity or religion changed with time and dramatically on occasion. As someone who studies Czechoslovak history, I do not feel comfortable at all calling Prague--at times a German city, a Catholic city, and, prior to the Second World War, the capital of the only liberal democracy in Central Europe (on top of being due south of Berlin)--an "Eastern European" city. The consensus on Eastern Europe seems to be that there will never be a consensus on its exact boundaries.
Despite this ambiguity, people commonly refer to "Eastern Europe" and "Western Europe" according to the division that was artificially created during the Cold War. All of the European nations that the Soviet Union liberated at the end of the Second World War became a part of the "Eastern Bloc" politically dominated by Moscow. And while this division ignored historical trends--again, the Czechoslovaks perceived themselves as allies of the Western democracies prior to the war--it created for the first time a clearly definable definition of "Eastern" Europe. This definition is, of course, obsolete (without breaking the twenty year rule, we can still look to the integration of nations like Poland and the Czech Republic with "Western" Europe in the immediate wake of the Cold War as evidence of this, and of course the reunification of East and West Germany renders the definition completely useless), but it was an extremely important and clearly-defined division for much of the twentieth century. The so-called "Iron Curtain" divided Europe into two camps, both threatening the complete obliteration of the other if another major war emerged in Europe. Thus it continues to linger in the American mind (I have broken the twenty year rule with this last statement, to be sure).
Most recently west and east has been used as a cold war era designation, but in my opinion the earliest de facto use of an east/west divide comes around the time of the germanic conquest to the north and south of the various german(ic) principalities between the years 1000 and 1300 AD.
Chronicles involving the territory east of today's poland draw a distinction between the catholic german(ics) and the pagan finno-ugric, balt and slav peoples. This distinction of east and west in some form usually between germanic states and russo (later russian) territories has persisted up until the modern era.