A fiber pigtail is a single, short, usually tight-buffered, optical fiber that has an optical connector pre-installed on one end and a length of exposed fiber at the other end.
The end of the pigtail is stripped and fusion spliced to a single fiber of a multi-fiber trunk. Splicing of pigtails to each fiber in the trunk “breaks out” the multi-fiber cable into its component fibers for connection to the end equipment.
Pigtails can have female or male connectors. Female connectors could be mounted in a patch panel, often in pairs although single-fiber solutions exist, to allow them to be connected to endpoints or other fiber runs with patch fibers. Alternatively they can have male connectors and plug directly into an optical transceiver.