The weakening of the Soviet Union had a profound impact on European countries, especially Eastern European countries which were under the infamous 'iron curtain'.
In a nutshell, the weakening of the Soviet Union directly lead to:
1. Less support for Socialist and Communist parties all over Europe
2. A rise in the demand for democratic values
3. An indirect in the demand for human rights and freedom of Speech
4. A decrease in military tensions alongisde the Iron Curtain.
The eventual collapse of the Soviet Union significantly decrease the influence of Russia as a political and cultural force in Eastern Europe.