Cyprus's banks are more than just dumps for dirty Russian money. is a banking hub for a variety of entities who want to do business with Europe. They help western Europe and Russia (and, more recently, emerging markets) invest in each other, get stocks listed on each others' exchanges, comply with the applicable financial regulations, and things like that. They do lots of "financial services" and consulting.

Or they did, anyway.

Wikipedia: "As a result of the reforms in the past decade Cyprus has developed into one of the world's more important international business centers. In the years following perestroika it gained great popularity as a portal for investment from the West into Russia and Central and Eastern Europe."