Imam Hussain who is the prophet Muhammad’s grandson was martyred on the tenth day of Muharram, day of Ashura, in Karbala but why do we have a ten-day of mourning period started from the first day of Muharram?!
Recently, professor Panahiyan, an Iranian cleric who teaches at the universities and Howzah, answered this question as a note to a news channel that I tried to translate the main parts of it:
There might be some different reasons for mourning form the first day of Muharram. It might be because of what Imam Reza, the 8th beloved Imam of ours, said about his father, Imam Kazem (pbuh): “No one could have seen my father’s smile when the month of Muharram came. Sadness was increasing in his face day by day till the tenth of Muharram and when the tenth day of Muharram would dawn, it would be a day of grief and weeping for him.“
Another reason might be that mourners can prepare themselves for the deep grief of Ashura by mourning form the beginning of Muharram because the grave tragedy of Ashura can be more tolerable after one week of mourning. The prophet Muhammad said that “surely , there exists in the hearts of the believers, with respect to the martyrdom of Husayn, a heat that never subsides.” Thus, Every one who feels this heat, knows that entering to the day of Ashura without a previous mourning period is very painful.
For some people a ten-day of mourning period is an opportunity helping them to feel the great tragedy of Ashura.
Actually this mourning period might be a type of volunteering to help not mourning and it seems to us that mourners go into Imam Hussain’s tent from the first day of Muharram in order to help him and not to leave his leader alone. That’s why this period of ten days is like an epic while mourning on Ashura night has just a color of sadness and greif.
 (کَانَ أَبِی ع إِذَا دَخَلَ شَهْرُ الْمُحَرَّمِ… امالی صدوق/128)
 «إِنَّ لِقَتْلِ الْحُسَیْنِ حَرَارَةً فِی قُلُوبِ الْمُؤْمِنِینَ لَا تَبْرُدُ أَبَداً»مستدرک الوسائل/10/318