Help me identify this type of pin header
It's a female pin header, most likely 0.1"/100mil/2.54mm (but use your calipers to verify). The little metal pins are for soldering into a PCB, whereas the corresponding male connector plugs into the contacts embedded within the plastic housing.

Also note that they are available in "stackable" form, where the metal pins are long enough for the connector to act as both male and female; these are used on both PC/104 expansion boards and Arduino shields so that they can be stacked multiple devices high.