You can also use those pieces to make simple or complex patterns. You can make piles and talk about which is bigger or smaller. You can talk about adding or taking away. Sometimes you might create new shapes by combining the pieces, i.e. two squares to make a rectangle or two triangles to create a diamond. When pieces come in various sizes, you can arrange them from smallest to largest.
Picture puzzles offer many opportunities for a variety of play experiences.
You can talk about colors and shapes or clues that will link one piece to another. You can take out only as many pieces as the child is old, taking turns putting back different parts of the puzzle, before doing the whole thing. As the puzzles become more difficult, you can talk about inside and outside or border pieces. You can call attention to specific details. These are all pre-reading skills.