Why do some Shia Muslims flagellate themselves at Ashura?

Next week, Lebanese Shia will commemorate Ashura, which marks the death of Hussein ibn Ali, the grandson of Prophet Muhammad, at the battle of Karbala (modern-day Iraq) in the year 680. The commemoration takes place on the 10th day of the Muslim calendar (“Ashra” means 10 in Arabic). 

The day is marked with mourning rituals: Shia men and women parade through the streets slapping their chests and chanting. But the most memorable scenes, though not the most common ones, are of some Shia men flagellating themselves with chains or cutting their foreheads until blood streams from their bodies: they seek to emulate the suffering of Hussein.

Some Shia groups, Hezbollah being one of them, discourage the bloodletting. They encourage people to donate blood instead: Haret Hreik municipality organized a Ashoura blood donation today.

For the record, Sunni Muslims too commemorate Ashura, but for them it is to mark the day Noah left the Ark, and the day that Moses was saved from the Egyptians by God.