It is named for its resemblance to a finger and is a type of cold trap.
The device usually consists of a chamber that a coolant fluid (cold tap water, or perhaps something colder) can enter and leave.
Many commercially available rotary evaporators can be purchased with a cold finger in place of a Dimroth condenser, for example.
When used as a condenser in a rotary evaporator, cold fingers can be cooled to a lower temperature of −78 °C (dry ice), compared with water condensers that can be cooled to −40 °C (ethylene glycol/water mixture).
The lower temperature achieved reduces the quantity of volatile material exhausted into the air.