I'm gonna tackle this from the classical mixing engineer working with a recorded band perspective:
Panning is a way to give the listener the impression that they are listening to a live band in front of them, not a pile of waveforms stacked on top of each other. When you go see a band live on stage, are they all standing in marching formation, single file?
Of course not! They're spread out, so that the sound waves of their instruments are not blocked by or overlapping another instrument. Even the drummer's kit is not all directly down the center: the kick drum is near the center, the hat is usually off to the left, the snare is a little to his right, and the toms and cymbals are placed in a panoramic position (more for the drummer than the listener, but hey). The singer? Usually right in the middle, with the drum kit behind them or off to one side.
It's your job to recreate that positioning so when a person closes their eyes, they could visualize where the band members are standing on stage. They can tell the difference in location between a high tom and a low tom. All these little tiny things that individually are barely noticeable, but come together to provide this beautiful sonic picture that helps a song feel complete and polished.