Rough terrain underground would be things like rubble and other obstructions, thick mushroom clusters, etc... Much like the above ground version. Depending on what it is you can use larger rocks, wood chips (which are lighter, pillars, vines, etc...
Page 107 covers the issues of hazards and light. As for movement, treat it the same as listed for rough terrain, ie- movement is halved.
As for running, if the terrain is limiting because it is rough, the model may not run. If the model has a skill that allows passage at regular movement through rough terrain of a certain type, they still may not run. The XX Warrior descriptions should have specified that better.