The skill is used when a compound has decayed to 0% and the buildings within it have deteriorated, possibly to the point of being unusable. You may "Attempt to repair this X" (on the building's utility menu) every 60 seconds. If you succeed, the building's condition will improve (by one level?) and you may try again immediately.
Speculation is that this skill is like Tale1's Mechanics skill - every skill level allows you to fix one 'bit' on a building (specific to a character, so you might be trying to fix the same bit as someone else if it doesn't work).
Each type of school offers a different facet of the the skill.
So far that is
Buildings list a descriptive condition that tells how badly it has decayed. Conditions so far found from worst to best are:
Note: If you are repairing FROM almost usable to servicable, the building will still be disabled until you repair it to good. If it deteriorates from good to servicable, it will still be usable however.