This term is most commonly used to refer to the situation in which a political entity that has been at least relatively united splits up into smaller parts. This is, for example, something that happened in many communist countries after the fall of communism. There are indications (see link below) that it might happen in the European Union and even in the nation of Belgium.
What happens in political disintegration is that various parts of a political entity come to feel that their differences are too serious to be overcome by whatever similarities they feel. This often happens when a country is made up of people from different ethnic groups. In the case of the EU, it could happen because that political entity is made up of a group of sovereign nations that have many historical, ethnic, and cultural differences.