A learned society is a group of grown-ups who really like a particular subject, like science, history or literature, and they want to learn and share more about it with others. It's like a club where everyone has an interest in the same things and wants to help each other learn more.
They do this by having meetings, where they talk about their favorite subjects, share what they've learned, and even present research they've done or new ideas they have. They might also publish books or journals on the subject so that other people can learn from what they've discovered.
When grown-ups are part of a learned society, they get to meet other people who are just as interested in the subject as they are. They can learn from each other, share their knowledge, and even make new friends! It's like having a group of people who really support and appreciate what you're interested in.