The suspension clause was written into the EU Treaty (Article 7) by the Treaty of Amsterdam.
Under this clause, some of a Member State's rights (e.g. its voting rights in the Council) may be suspended if it seriously and persistently breaches the principles on which the Union is founded (liberty, democracy, respect for human rights and fundamental freedoms, and the rule of law). But its obligations would still be binding.
The Treaty of Nice added a preventive mechanism to this procedure. On a proposal by one third of the Member States, by the Commission or by the European Parliament, the Council, acting by a majority of four fifths of its members after obtaining the assent of the European Parliament, may determine that there is a clear risk of a serious breach of these fundamental principles by a Member State, and address appropriate recommendations to it. Article 354 of the Treaty on the Functioning of the European Union (TFEU) provides the voting procedures to be used by the main European institutions when a Member State faces application of Article 7 of the TEU.