Image 1 Caption: The gravitationally-bound Pluto-Charon system.
Features:
We neglect the small moons in the rest of this explication of the Pluto-Charon system.
To 1st-order, the barycenter defines an inertial frame for the Pluto-Charon system and the Pluto system as a whole.
If you are at a given location on the side of Pluto/Charon facing Charon/Pluto is always in the sky at the same position relative to the ground for your location. If you are on the other side of Pluto/Charon, you never see Charon/Pluto.
Image 2 Caption: "An animation showing an oblique view (more exactly a view at high inclination) of the orbits of Pluto and Charon. Note Pluto and Charon are mutually tidally locked to each other, and so always turn the same side to the other. Charon is massive enough that the center of mass (AKA barycenter) of the Pluto system (which includes 4 other small moons which have little effect on the location of the center of mass) lies outside of Pluto, and thus Pluto and Charon are sometimes considered to be a binary system." (Somewhat edited.)