The phrase "to complete the puzzle" means to find all the missing pieces and put them in the right places so that the puzzle is finished and makes sense. Full definition
Using a clear, precise event marker is one important piece of completing the puzzle that makes sure that trainer and learner are all on the same page. (karenpryoracademy.com)
Complete the puzzle by filling each block with the letters for the correct terms. (thoughtco.com)
I did find that I had some issues while trying to complete the puzzles in first - person. (the-gamers-lounge.com)