Celebrating Ashura and Hijrah is considered as sunnah kauniyah. That is observing a natural phenomenon of the universe. Every day is never the same. By nature each thing has its own uniqueness. For instance Ashura. It originated from an event of bygone years when the Jews observed fasting on the day.
There is a verse in the Qur'an asking us to remember 'the days of Allah'. There are indeed special times or days that teach us lessons regarding acts of devotions. The episode of Siti Hajar walking back and forth between Safa and Marwah gave rise to sa'e as a rite required in pilgrimage. Prophet Muhammad's habit in fasting on Mondays (his birthday) tell us of the needs to celebrate a meaningful event. The lesson we learn from these examples is that we are encouraged to look for times/days which are deemed to be special - the times/days chosen by Allah for us to multiply our ibadah.
So we know that Prophet Muhammad used to fast for two days during Ashura and on this special occasion we are also encouraged to treat our families, give to charity, help the poor and show kind gestures to orphans.
Other than rejoicing in Prophet Musa's victory over Firaun, we also mourn over the death of Sayyidina Hussain - a tragedy foretold by Prophet Muhammad. Hussain bin Ali was his beloved grandson, one for whose sake Nabi would extend his prostration for fear that Hussain might fall off his neck. Unfortunately, the Shi'ah has gone overboard in glorifying Hussain.
Having understood the significance of Ashura, we must know how to balance between its joy and sorrow.
Habib Zain ended his tausiyah by singing a qasidah composed by Shaykh Amir Kurtubi. And the audience was left mesmerized, emotionally and spiritually.
p/s O son, we've been taught to recite Hasbunallah wanikmal wakil nikmal mawla wanikman nasir 1000 times on Ashura. So you do the same.