the president didn't resign. The government (ie the prime minister resigned) after the assassination of ex prime minister rafik hariri. the president of the republic is still in place.
The prime minister Omar Karame who resigned monday in the parlement after a heated confrontation with the opposition members of the parlament, in a historical extraordinary parlament session that was broadcasted live on TV and on the radio amid massive manifestations in martyr square in Downtown Beirut. Omar karame resigned due to the extreme pressure exercised by the opposition about the incompetence of the lebanese autorities in handling the investigations of the assassination of Rafik Hariri, as well as the growing popular support the opposition was gaining. CNN labeled this resignation as an example of people power, given the pressure that the population was able to exercise peacefully demanding the resignation of the government