narrated ibn abbasرضي الله عنه the prophetصلي الله عليه و سلم came to al madina and saw the jews fasting on the day of ashouraعاشوراء he asked them about that . they replied,< this is a good day, the day on which allahالله rescued bani-israel from their enemy , so musa<moses> observed saum <fast> on this day>. the prophetصلي الله عليه و سلم said,< we have more claim over musa< moses> than you>. so the prophetصلي الله عليه و سلم observed saum<fast> on that day and ordered < the muslims> to observe saum<fast> <on that day>.                                                                     sahih al boukhari

abu qatadahرضي الله عنه reported : the prophetصلي الله عليه و سلم was asked about the observing of as-saum< fast> on the 10th of muharrem< day of ashoura> and he replied , < it is an expiation for the sins of the preceding year>.                                 riadh assalihin