Dissected puzzles were the forerunners of jigsaws. They were very simply made by placing a picture on a piece of wood and cutting it into shapes. Some pieces might interlock, but most of the puzzle was just pushed into place. This meant that it would not stay in one piece very easily. To solve this, the outer edges of some puzzles, like this example, had long interlocking pieces that would hold the whole puzzle together. The reverse of this puzzle has a map of England and Wales. It was quite common for a puzzle to have two sides. These were called double dissection. Reference: Victoria and Albert Museum
Dissected puzzles are very collectible and there are some beautiful examples. Values of dissected puzzles depend on condition plus subject matter.
Below are some examples and price guides of some dissected puzzles including a John Spilsbury puzzle and a boxed set of Victorian puzzles with pictures of children in Victorian dress.