To mourn the death of a public official.
Traditionally this is when someone dies
Flags Are At Half Mast to Honor A loss of someone who died for our american flag.
Chicago Bears fly flags at half staff to honour the anyone that died during the service to their city or country, most recently this was done to honour the death of 19 fire fighters that died.
The US government flag flying flags at half-staff on April 15, 2014 is in honor of Sergeant Timothy Wayne Owens who died during the Fort Hood shootings.
Only the President or a state Governor can order when and for how long the American flag is to be flown at half-staff on government property.
Formerly half mast (Navy) and half staff (Army) were to honor deceased VIPs (Very Important People-US Military & Government Personnel). Today, that tradition has been expanded to many (civilian) people and many events.
The reason flags are half mast on Sydney Harbour Bridge is most likely because someone has died. Flying flags at half mast is a form of respect for someone that has died.
I was just there today and it and the Texas flag were both being flown at half staff
We were told the son of a business man who owns KFC and Taco Bell was killed. The flags at these locations (N1) were at half staff.
Recently the flags are at half mast because of the shootings in Atlanta and Colorado. :-(
In the United States the flags are flown half-staff by order of the President for any amount of time he wishes. However by law 30 days after the death of a current or former president and 10 for vice presidents.
By convention flags are flown at half mast during a period of official mourning (e.g the death of a national leader or a for national tragedy). It is a mark of respect.