A stylized puzzle piece that forms the "H" of the word handicraft should underline the fact of building things by your hands. Even as a child, you can begin putting things together step by step. Pieces are fitting together. They link to each other. These are the main aspects of handicraft in my opinion.
It is also a sign that stands out from other handicraft-logos, using hands, tools etc.
It’s more like a metaphor and also works perfect as an on-going piece by piece award trophy.