A walking foot is a special sewing machine presser foot with built-in feed dogs that grip and advance the upper layer of fabric as it travels through the sewing machine. The movement is in unison with the machine's feed dogs, which grip the underside of the fabric. The action of this special presser foot helps keep the layers from shifting apart as they move through the sewing machine.
A walking foot is essential for pucker-free, straight line machine quilting. It is also a helpful when sewing together the multiple layers of a rag quilt, when you make a denim quilt, and when you sew binding to a quilt.
Many sewing machines come with a walking foot made by the manufacturer, and when it isn't included, the manufacturer usually offers a walking foot as an option. Generic versions that work with most other sewing machines are available, too.
A walking foot is sometimes called an even feed foot.