Sawtooth hangers are attached to the back side of a picture frame, usually placing just one at the center of the top rail, with the serrated "teeth" of the hanger facing downward. These serrations allow the frame to be hung on an ordinary nail in the wall.
For drywall walls, sawtooth hangers are probably the least secure of all picture frame hanging methods, but they are perfectly adequate for small or lightweight picture frames.
The potential weak point is usually not the sawtooth hanger itself, but the hanging nail driven into the wall. Nails can come loose or tear out of drywall, so make sure that the nail you install in the wall is not loose or wobbly before you hang a frame with a sawtooth hanger on it. Wood paneling and similar wall surfaces are less of a problem as they will hold a nail firmly.