Ordinance or law coverage pays the added cost of bringing a damaged building up to current building codes when you repair or rebuild after a covered loss. A standard property policy pays to restore what was there before, but local codes may now require costlier materials or methods, and that gap is what this coverage fills.
It matters most for older homes, since codes change over time and a rebuild often must meet stricter current standards.
Example: a fire destroys part of an older home's wiring. Current code requires a more expensive electrical system than the original, and ordinance or law coverage pays that upgrade cost the base policy would not.
Related: dwelling coverage, replacement cost, peril. See the homeowners insurance overview.