A walking foot is a mechanism for feeding the fabric through a sewing machine as it is being stitched. It is most useful for sewing heavy materials where needle feed is mechanically inadequate, for spongy or cushioned materials where lifting the foot out of contact with the material helps in the feeding action, and for sewing many layers together where a drop feed will cause the lower layers to shift out of position with the upper layers.
A sewing machine might have a single walking foot, or two walking feet with alternating action. A walking foot may be combined with another feed mechanism, such as a drop feed or a needle feed.
Only a very few household machines have a walking foot, but this type of feed is common in industrial heavy duty machines. Some household machines are marketed as having a walking foot, but actually have a puller feed. However, almost all household sewing machines use a standard connector for their presser foot, and so add-on walking foot attachments are available.
Here is a video demonstrating a walking foot:
A quick article by Suzan Michaels about the Walking Foot:
A walking foot sewing machine is often an industrial-type machine that accurately and precisely sews layers of fabric with no slipping or puckering of seams. The two-piece foot feed moves one side at a time, and appears to be "walking" as it feeds the fabric under the needle.