This is an expression of their grief on the death of their favourite leader Hussain, considered to be the representative of Allah.
While Shia Muslims consider Muharram to be a sorrowful occasion, Sunni Muslims observe it as a festival and look at Ashura as a happy day though the religious aspect remains intact.
Pious Sunnis keep a roza(fast) on Ashura as per the Hadith of Prophet Muhammad.
According to the Hadith, the Prophet saw the Jews fasting on the 10th of Muharram to commemorate their liberation from Egyptian slavery and the extermination of the army of the Pharoah in the waters of the Red Sea.