Packing means putting dressing material inside the wound rather than only over it. It is one step in wet-to-dry dressing changes: place the gauze pads or packing tape in your wound, carefully filling in the wound and any spaces under the skin.
There is a precise boundary that is easy to get wrong: avoid putting the moist gauze onto the skin; put it only into the wound. Moist material sitting on intact skin is a separate problem, and the instruction exists to prevent it.
The packed material is then covered. Cover the moistened gauze or packing tape with a large dry dressing pad, held in place with tape or rolled gauze.
Why pack at all? An open surgical wound heals from the inside to the outside, and a dressing helps absorb drainage and keeps the skin from closing before the wound underneath fills in. Packing is how a wound with depth, or with spaces under the skin, is kept open and absorbing while it fills.
In a wet-to-dry dressing specifically, the packing is doing a second job as it comes out. A wet or moist gauze dressing is put on the wound and allowed to dry. Wound drainage and dead tissue can be removed when you take off the old dressing.
There is a measure of progress built into this. As the wound heals, you should not need as much gauze or packing gauze.
Packing is taught by the people managing the wound, and the amount and the material are chosen for that wound. Nothing here is a substitute for being shown.