Puzzles tease the brain, test memory, and keep occupied those who have time to lose track of time. There are many types of puzzles: brain teasers, crosswords, word finds, logic puzzles, jigsaws, etc. Jigsaw puzzles, in particular, practice and test brain function. They are also a hobby for those who easily become bored on a rainy day. The benefits of jigsaw puzzles are numerous, and can lead to better overall quality of life.
To begin with, puzzles prevent boredom. Now there are certain people this doesn't work for (imagine the young child who loves to play outdoors loudly). They do require a certain level of patience that younger kids don't have. For example, puzzles were big with my family at the beach, but we'd usually do them once we were back from a long tiring day of swimming and sitting in the sun and sand. We used them to relax in the air conditioning. My cousins might come over and try to place a few pieces, but usually they'd go right back to swimming in the pool once they got frustrated with pieces that just wouldn't fit. Anyway, puzzles prevent boredom by keeping the brain occupied enough while letting the body relax. Similar to reading a good book. On the other hand, reading occupies a lot of brain space, while the visual and tactile pursuit of putting together a puzzle leaves plenty of space open for conversation or thinking about other things. I used to do big puzzles in the summer time (1000-2000 pieces) and I'd sit on the porch all day organizing and putting together sections while drinking bottled coke and eating pretzels. It required just enough brainpower to keep it active and alert during the long months I wasn't in school.
Jigsaw puzzles require strategy and memory to put together. The eyes and brain work together to determine it is easiest to start with the edges of a puzzle because that flat side is the easiest to recognize. On another beach trip with my family, we started a huge 10,000 piecer by searching out the edges. We had been working for days and finally completed the edge when a rainstorm blew onto the porch and the puzzle was scattered. I was young then, and too disappointed to start over with all those edges, but some of the adults kept working. I don't think we finished that puzzle though. Once those edge pieces are identified, the eyes move on to definable patterns in line or color (a large pink flower means all of the pink pieces go in the same place). We use clues, like the picture on the box and the patterns on the pieces to test out possibilities. When we get to difficult place, the shape of the pieces starts to matter. For example, in a puzzle with a ton of blue sky might require greater focus on the fading in and out of the blue or we may have to try every piece of a certain shape if they're all the same color. Especially at the end of a puzzle, it is easy to just test every piece in every space because there are only so many combinations. This requires some organization of the pieces so that each is tried and set aside.
Memory comes into puzzles, too. When you've been looking at the same pieces for a while, you start to remember the weird looking ones or the ones you've already tried. The brain picks up patterns in the pieces and knows not to try certain ones again. You also go looking for new pieces of the same type when you register that all the combinations have been tried. When something happens to test accuracy, like two sections don't fit together because of one piece, the brain is at disequilibrium, and so it tries to fix the problem by identifying which piece was put in incorrectly. This requires a great attention to detail that has come from testing memory to be more and more specific. When you first start a puzzle, it is much easier to make a mistake in putting together two pieces that seem alike because you haven't been looking with such specificity. Eventually, many people don't have to look at the box anymore.
All of this memory and brain function testing, multitasking and socializing time, and occupying of free time and relaxing lead to better quality of life. Doing all types of puzzles is scientifically proven to reduce likelihood of acquiring memory diseases like Alzheimer's and dementia, cancers of the brain, and anxiety disorders. Of course doing puzzles doesn't automatically guarantee a healthy life (exercise, nutrition, and companionship are also important), but it is a step in the right direction for adults who are easily bored or have trouble relaxing. I've been doing puzzles my whole life (all the types, not just jigsaw) and I still get automatically "in the zone" every time one is placed in front of me. I enjoy games with some puzzle element more than skill requirements. Some of my most vivid memories are of doing puzzles by myself or with my family (perhaps because my eyes were so active and it was easy to listen). My quality of life has been improved through puzzling, and I encourage anyone who's never tried to be open to the benefits.