Obstacles block region exits. As such, they are considered to occupy regions on both sides of the exit. When an Obstacle is defeated (commonly through damage or Lockpick), it no longer blocks the exit. Sometimes other Challenges can move freely through Obstacles; the scenario design will specify when this is the case.
Some Obstacles have the Persist keyword, which grants them seperate EP totals (and defeated statuses) for each PC. Such Obstacles recover their EP to full for a given PC whenever that PC Moves, even if it was defeated for that PC.
Some Obstacles have the Climbing keyword; such Obstacles generally also Persist. Climbing Obstacles have Height values associated with them, which add falling damage and other properties. See the linked pages for more information.
If an Obstacle has a Lock entry, it can be instantly defeated by a PC who wins an opposed roll with a Lockpick entry. Such Obstacles rarely Persist, but if one does, it would only be considered defeated for the PC who wins the Lockpick roll.