Traverse means to move through a border. For example, Wall of Brambles specifies that it sits atop a border of a site. Perilous Bridge has a passive ability which affects its top border. To move through a border, a unit must take a step which causes it to enter a location on one side of the border, having occupied a location on the other side of the border.
Some effects use the phrase 'traverse on the ground,' e.g. Wall of Brambles. To 'traverse on the ground,' a unit must move from the surface of a site to the surface of another site, excluding Airborne and Teleportation.