As Cyprus is a candidate country bound to join the Schengen Area, Residents of non-EU countries who hold valid multiple-entry Schengen visas must first pass through a full Schengen member territory in order to utilize the visa in Cyprus. The Schengen Visa holder is allowed to travel to Cyprus directly from a Schengen member country without applying for a National Cypriot visa and stay in the Republic of Cyprus for the duration of their Schengen visa.
The above arrangements do not apply for persons holding a Turkish or Azerbaijani passport. If you are affected, please visit the Cyprus Ministry of Foreign Affairs website on how to apply for a Cyprus Visa.
For further information, please check the European Commission website regarding Schengen Visas.