Mike- The packing tool is used on the hair after it's tied onto the hook shank, not before. When using the washer, tie in your clump of hair as usual, put in a few half-hitches, and then slide the washer over the hook eye and up against the half-hitches. With the washer, cram the most recently tied in clump of hair back down the hook shank into any clumps that are already tied in. This can create a very durable, dense, and buoyant fly. Repeat as necessary after the tie in of every clump.
Regular packing tools are used for the same effect, but the packing may not be as even as what a washer can yield.
Hope this clears things up a bit.