The Space Station Remote Manipulator System (SSRMS) is a seven-jointed teleoperated manipulator used on the International Space Station (ISS). Each end of the manipulator is composed of a Latching End Effector (LEE) which serves a dual purpose: to grapple payloads, and to mount the manipulator on the ISS.

The LEE can only attach ("grapple") to specially provided points on the ISS and payloads ("grapple fixtures"). The grapple fixtures come in several different flavors. Simple payloads might have a Flight Releasable Grapple Fixture (FRGF), the simplest flavor.

This grapple fixture provides only a mechanical interface for the LEE. The LEE incorporates a rotating, retractable carriage fitted with snare wires. During a grapple, the SSRMS is positioned so that the grapple pin at the center of the fixture enters the LEE. When a capture is commanded, the carriage rotates to wrap the snare wires around the shaft, then retracts, pulling the wires against the knob at the end of the shaft to provide tension to hold the interface tight. The three curved metal bars around the grapple shaft provide rotational alignment and stability by interfacing with the semi-circular cutouts in the outer ring of the LEE. The black and white object at the top of the grapple fixture is a camera target which aligns with a camera on the LEE. Here is a schematic of this grapple sequence, from here.
To base the manipulator on the ISS, this simple grapple fixture is insufficient, because it does not provide any power or data connections. In this case, a Power Data Grapple Fixture must be provided.
While similar to the FRGF, it provides in addition, the four rectangular interfaces around the circular feature. Behind the doors of these interfaces are provisions to receive latching umbilicals which can extend from the LEE. These umbilicals provide a stronger mechanical connection than the snare wire/grapple shaft interface, and also contain connectors which allow for the flow of power and data into and out of the interface. You can see the umbilicals mounted around the LEE in this picture (which was taken with the insulating blankets removed).

The PDGF also has a "curvilinear coupling" - the circle of square black teeth - that interfaces with the similar coupling on the LEE to provide additional resistance to rotational forces when grappled.
To grapple a PDGF, the sequence proceeds as described above. Additionally, after the carriage is ridigized, the umbilicals extend through the flipper doors on the PDGF, attach mechanically, and connect up the power, data, and video lines. The tension can then be removed from the snare wires to reduce the strain on the LEE mechanisms.