The Republic of Cyprus is a member of the European Union but has not yet fully joined the Schengen area. That means a separate national visa is required to enter the country.
The main difficulty is that Cyprus has no embassy in Baku, and consular services for Azerbaijan are handled through a mission abroad. The route of the application and the way documents are sent therefore need to be settled in advance.
There is one important exception: under certain conditions, holders of a valid multiple-entry Schengen or other EU visa can enter Cyprus without obtaining a separate visa. This rule changes often, so check it before you travel. Viza.az looks at the visas you already hold and works out the shortest path.