a simple nick name referring to the fact the person fits like a puzzle piece. this can be referring to perfect proportionality such as a hug. it should be taken as a term of endearment seeing as puzzle pieces are perfect matches.
it is similar to saying two pees in a pod, yet far more loving. a complete term of endearment.
Man i'm just looking for my puzzle piece.
Kaylee you are my puzzle piece.
dude, when we hug shes just a perfect puzzle piece