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]
(..) Tell me about Peralta. Jacob Peralta is my best Detective. He likes putting away bad guys and he loves solving puzzles. The only puzzle he hasn't solved is how to grow up. That was very well put. I've talked a lot about Jake in my departmentally mandated (..)2013 TvShow: Brooklyn Nine-Nine Title: Pilot Season: 1 Episode 1