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]
(..) - Why kill Tanya? I don't want Tanya. I want what's inside her. No! - And the others, why kill them? - They were all... ...pieces of the puzzle. Pieces of the vaccine. Stop this! Answer. Come on Prue, pick up. There's no answer. It's after . It's going straight to voice mail. (..)1998 TvShow: Charmed Title: The Truth Is Out There... and It Hurts Season: 1 Episode 8