Obstacles are objects around your shelter that need to be removed or repaired in order to expand your shelter. Removing or repairing them costs Credits, Stone and Metal, and requires a Builder's time. They can be completed quickly for Nanites, but its usually better to just remove them slowly as needed.
¶ Rocks
Rocks are the most common type of obstacle and they can be seen throughout the underground portion of your shelter. The cost of removing them varies between each group of rocks, but there is no rush to remove them all.
¶ Broken Bridge
Behind the building portion of your shelter is a large hill. Your shelter can expand into this hill, and then downward underground by first repairing the broken bridge behind the building. This is a good way to open up a lot of space for more rooms.
Note: For some reason repairing the bridges now costs more Stone and Metal than is possible to store - not sure if this is a bug or intentional.