The "intermediate social entities" are those organizations that grow naturally out of the social, economic, and political interactions of people:
This is the realm of civil society, understood as the sum of the relationships between individuals and intermediate social groupings, which are the first relationships to arise and which come about thanks to "the creative subjectivity of the citizen". This network of relationships strengthens the social fabric and constitutes the basis of a true community of persons, making possible the recognition of higher forms of social activity. (section 185)Subsidiarity has both positive and negative senses. In the positive sense, larger entities should offer whatever assistance is necessary for smaller entities to flourish. In the negative sense, larger entities must not do anything that would prevent the smaller entities from flourishing. "The principle of subsidiarity protects people from abuses by higher-level social authority and calls on these same authorities to help individuals and intermediate groups to fulfil their duties" (section 187).
A denial of the principle of subsidiarity "limits and sometimes even destroys the spirit of freedom and initiative", which is why it is "opposed to certain forms of centralization, bureaucratization, and welfare assistance and to the unjustified and excessive presence of the State in public mechanisms" (section 187).
In order for the principle of subsidiarity to be put into practice there is a corresponding need for: respect and effective promotion of the human person and the family; ever greater appreciation of associations and intermediate organizations in their fundamental choices and in those that cannot be delegated to or exercised by others; the encouragement of private initiative so that every social entity remains at the service of the common good, each with its own distinctive characteristics; the presence of pluralism in society and due representation of its vital components; safeguarding human rights and the rights of minorities; bringing about bureaucratic and administrative decentralization; striking a balance between the public and private spheres, with the resulting recognition of the social function of the private sphere; appropriate methods for making citizens more responsible in actively "being a part" of the political and social reality of their country. (section 187)Various circumstances may require that the State step into what would otherwise be the functions of the smaller entities, e.g., to stimulate the economy or to address issues of injustice. "In light of the principle of subsidiarity, however, this institutional substitution must not continue any longer than is absolutely necessary, since justification for such intervention is found only in the exceptional nature of the situation" (section 188).
Compendium of the Social Doctrine of the Church
Wikipedia entry on subsidiarity