Double-running stitch is an embroidery stitch which starts as a running-stitch which doubles back on itself. This results in a reversable pattern. The look is somewhat like a modern sewing machine stitch (if the top and bottom thread are the same color). The difference is that the modern stitch has a top thread and bobbin thread which each stay on their own side of the fabric, whereas in double-running-stitch each thread works its way back and forth to each side.
One typically sticks every other segment on a pattern on the top on the way out then reverses direction and fills in the empty spaces on the way back. Often patterns require side trips which may need to be done completely either (on the way out or the way back).
This stitch is used in blackwork embroidery. The portrait painter Hans Holbein the Younger became court painter to Henry VIII, and he painted Henry's queens wearing dresses richly decorated with Blackwork. The double-running stitch employed in Blackwork is often called Holbein stitch.