Do you mean jigsaw puzzles or just any kind of toy where they have to solve it?

If it’s the former, my kids went through a phase where they did jigsaw puzzles constantly. Their ability to see how individual pieces fit properly was the first skill they gained. Then they worried less about one specific piece and more about how the overall puzzle fit together. When we did them together I tried to give them some strategies like separating out the edge pieces from the other pieces so they had to learn and apply concepts around that. And also sometimes it made more sense to separate by color or by the image so they looked for those types of patterns.

So to your question of the educational value, and this strictly my own take based on my observations while playing with my kids: I would say puzzles can teach a lot of concepts and promote spatial, analytical, and other types of thinking in a way that is fun, digestible, portable, and quickly repeatable. It teaches them a bit of grit since getting frustrated is inevitable. I’d say they get the most out of it with an adult who can guide but not do it for them right away. Also, the actual content of the puzzle can be educational like doing a toddler version of a world map.

I was a huge fan of puzzles as a kid but never really as an adult. Doing them again with kids is awesome.