A jigsaw puzzle was a tiling puzzle that required the assembly of numerous small, often oddly-shaped, interlocking pieces. Each piece had a small part of a picture on it; when complete, a jigsaw puzzle produced a complete picture. Jigsaw puzzles were originally created by painting a picture on a flat, rectangular piece of wood, and then cutting that picture into small pieces with a jigsaw, hence the name.
After Captain Jean-Luc Picard, Klingon Captain Nu'Daq, and Cardassian Gul Ocett combined their DNA patterns they found out that one piece was still missing. Captain Picard compared this DNA program with a jigsaw puzzle. (TNG: "The Chase")
On stardate 47869.2, the USS Enterprise-D's holodeck was apparently malfunctioning. In fact, it was creating a lifeform with emergent properties. It re-enacted this process as various holodeck characters on a train doing different things. One of the more tangible representations of the lifeform's construction was several of the characters constructing a jigsaw puzzle of the lifeform. (TNG: "Emergence")
In 2377, Icheb began tutoring Naomi Wildman in her study of genetics. Taking the creative approach, he had her learn by putting together a jigsaw puzzle featuring an image of a strand of DNA. After nearly completing the portion of the puzzle showing the DNA helix, Icheb congratulated Naomi for having "recognized the complementary base pair," she admitted to him that "actually, I just found two pieces that fit together." Disappointed, Icheb told her that she was "missing the point," to which she argued, "I thought the point was to finish the puzzle," adding, "if you really want to help, find me a green piece that looks like Tuvok's ear." (VOY: "Shattered")