What is fansink?

Answer 1

A Fan sink is a Heat sink with a fixed FAN.

Heat sink's are blocks of metal, primarily used are are copper, and aluminum, that draw heat from a source ( such as your Processor, or another heat producing chip set ) and spread it across its surface area to be air cooled.

A Fan sink, combine's the heat drawing of it's sink with a dedicated fan blowing air into ore out from the heat sink below it. This will significantly improve the sinks cooling power.

So a processor cooler is most likely a Fan sink, but some chips surrounding it may only have a heat sink. ( Southbridge controller is usually placed near your CPU and is fitted with a black block of metal that has a lot of blades on it )