Prussia wasn't wiped off the map. The King of Prussia became the Kaiser of the German Empire after the Franco-Prussian war in the 1870's. Until the abdication of the Kaiser following World War 1, the whole of Germany was united under the Prussian King and the Prussian "junker" class pretty much dominated all kinds of things.

Prussia unified the German states in the German Empire in 1871. Almost fifty years later, Germany lost the First World War, and Poland was recreated from parts of the collapsed Russian and Austro-Hungarian Empires, as well as largely Polish territories taken from Germany. Polish nationalism was VERY strong, and it helped that Poles made up the bulk of the inhabitants in the area that became the Polish state after 1918 (with the exception of Eastern Galicia, the territory around Vilnius, and Eastern Poland).

After WWII, it had already been agreed that the territories taken from Poland by the Soviet Union in 1939 would not be returned. Instead, Poland's borders were to be moved westwards, and this meant an end to Prussia. Prussia had been seen by many as the source of German Militarism, viewed as the major cause of both World Wars, and so eliminating any potential influence on the future Germany (or Germanies as it turned out) was desirable. Poland needed to be territorially compensated, and to have a viable future economically. As a result, it was decided that all of Germany east of the Oder and Neisse Rivers, as well as the area around the city of Stettin, was to be rid of it's Germans; all 2 million+ of them.

East and West Prussia, as well as Posen, Upper and Lower Silesia, and Eastern Pomerania, territories that had been largely German, or at least in Posen's case German-ruled, for centuries were cleansed of their German populations, largely by force. Red Army and Polish Army troops evicted those that had not already fled the path of the invading Soviet armies. After the war, Poland became a satellite state of the USSR, a potential buffer against future western threats.

After the partitions, numerous Poles moved to Western Europe, primarily France, and brought the cause of re-establishing Poland with them. This ensured that it was at the forefront of discussion, especially during the nineteenth century when the era of romantic nationalism was developed.

Leading Poles also lobbied Western governments heavily during the First World War, notably Roman Dmowski. This was also helped by the fact that within the region of what is now Poland, there was an established Polish force, with military forces led by Józef Piłsudski (who was nominally serving the Austro-Hungarians, but effectively fought as an independent force against the Russians). These factors combined led to Woodrow Wilson adding the recreation of Poland as one of his Fourteen Points, and Poland's self-declared independence was recognised at the Paris Peace Conference.

Poles organized military organizations in all 3 partitions before WW1 and were very patriotic (naitonalist, whatever). During WW2 Józef Piłsudski created http://en.wikipedia.org/wiki/Polish_Legions_in_World_War_I - a Polish army out of them, they were part of Austro-Hungarian army, but had a degree of authonomy, and were used as bargaining card for greater Polish autonomy after the war.

Other powers fighting in WW1 also used Polish units: http://en.wikipedia.org/wiki/List_of_Polish_divisions_in_World_War_I

After Russia went communist, and Germany was defeated - Poles were the ones with the only remaining army in the region that still wanted to fight. Other armies were mostly demoralized and wanted to return home. Polish units took weapons from them, and waited for the recognition of Poland.