A jigsaw is a sharp power tool that's used for cutting curvy lines in wood or other materials. While most saws can only cut in a straight line, a jigsaw makes it easier to cut complicated patterns and shapes.
If you were making a jigsaw puzzle out of wood, you'd use a jigsaw. In fact, this is where the "jigsaw puzzle," (which is also simply called a jigsaw), got its name. The original meaning comes from the word jig and its sense of "up and down motion," which describes the way a jigsaw moves as it cuts.