Paths are lines that vector-graphics programs (like Freehand, Fireworks, Illustrator) use to determine how an image will be drawn when it is rendered. A Vector image is composed of paths, which could be thought of as blueprints for a drawing. The image shown on the screen is the result of those blueprints, but is always connected to them; thus, you can always change the image without losing quality by changing the blueprints. (To learn more about this type of image, called a "vector" image, see the NWE help page on the subject.)
The result is that drawing with Vector-based programs can be very different than drawing with a pixel-based program (like Photoshop). Every drawing you make becomes a path, meaning it can always be altered.
Here are a few pages about how to use paths.NOTE: These pages were made using images from Freehand. While most of these tools will work similarly in Fireworks, Dreamweaver, and Flash, there may be slight differences.