What is the unit of measure for a region's power supply?
They mean terawatt-hours.   Terawatts per hour is not a thing, but if it was, it would be TW/h.  

By 539.9 TWh in 2010 they mean for the entire year, i.e. 539.9 terawatt-hours/year.  Useful to economists, not useful to engineers.  But we can obtain plain terawatts.   

With 365.25 days in a year, hours/year is 24x365.25 or 8766.  

To get plain terawatts, we need to divide 539.9 terawatt-hours/year by 8766 hours/year...  yielding 0.06159 terawatts, or 61.59 gigawatts.  This number survives a sanity check; it's a perfectly realistic average generation for a country of that size.