The restaurant is trying to attract more customers, and the new menu is an important 'piece of the puzzle'. [=an important part of what is being done]
Ecologists no longer view different species as independent, but instead see them as pieces of the same 'jigsaw puzzle'.
His strange behavior is a 'puzzle' to his friends. [=his friends don't understand the reason for his strange behavior]
(..) discoloring them. I spoke to a dentist, Laszlo. Facts, figures, along with numerous suppositions. Pieces of a puzzle that right now lack form match no psychological outline. What we are missing, John, is not how he kills, but why. (..)2018 TvShow: The Alienist Title: These Bloody Thoughts Season: 1 Episode 4