Tirmidhi

1:
The tenth day of Muharram is called the Day of Ashura.
When the Prophet (sallallahu alayhi wa sallam) migrated from Makkah to Madinah, he saw that the Jews were fasting on this day.
He asked them, "Why do you fast on this day?" They replied, "On this day, Allah, the Exalted, granted Musa (alayhis salam) deliverance from Pharaoh, so we fast out of gratitude for this." The Prophet (sallallahu alayhi wa sallam) said:
"We have a greater right to Musa than you." Accordingly, he (sallallahu alayhi wa sallam) fasted on this day and also said, "If I remain alive till the next year, I will also fast on the 9th of Muharram along with it," so that there would be opposition to the Jews.
In fact, in one narration, he (sallallahu alayhi wa sallam) commanded: "Fast on the Day of Ashura and oppose the Jews—fast a day before it or a day after it as well."

1:
By "Yawm Arafah" is meant the 9th of Dhu al-Hijjah, when the honored pilgrims stand in Arafat and engage in remembrance and supplication. For them, this is the greatest act of worship on this day; therefore, fasting on this day is not recommended for them. However, for non-pilgrims, fasting on this day is of great merit. Through it, their minor sins of two years, which pertain to the rights of Allah, are forgiven. (It should be kept in mind that people living in regions far from Makkah should not fast on the 9th of Dhu al-Hijjah according to their local sighting, but rather should fast on the 9th of Dhu al-Hijjah according to the sighting of Makkah, because the pilgrims gather in the plain of Arafat according to that reckoning. However, where the horizon and country change, the people of that place should fast on their own reckoning of the 9th of Dhu al-Hijjah. In fact, it is better to fast continuously from the 1st to the 9th of Dhu al-Hijjah, because the virtue of deeds performed in these days has been mentioned abundantly in hadith, and the practice of the righteous predecessors (salaf salihin) in this regard is also mentioned in the narrations. And by this, the action upon Yawm Arafah as the 9th of Dhu al-Hijjah in the place of Arafat will also be fulfilled. And Allah knows best.

2:
If this objection is raised: How can the expiation of the sins of the following year occur when a person has not yet committed those sins? The answer is that the meaning of erasing the sins of the coming year is that Allah, the Exalted, will protect him from sins during that year, or He will bestow upon him such mercy and reward that it will serve as expiation for the sins of the coming year as well.

Benefits and Issues:
➊ The displeasure of the Messenger of Allah (sallallahu alayhi wa sallam) was due to the fact that he (the questioner) had asked for more than his own ability and strength. In this regard, no one can be equal to the Prophet (sallallahu alayhi wa sallam).

➋ The noble Companions (radi Allahu anhum) were well-acquainted with the temperament of the Messenger (sallallahu alayhi wa sallam), especially Umar (radi Allahu anhu). He knew how the Prophet’s anger could be appeased, and that was... by affirming the Lordship of Allah alone, the Messengership and Prophethood of Muhammad (sallallahu alayhi wa sallam), and the acceptance of Islam as the religion—even to the extent of expressing heartfelt contentment with it.

➌ Regarding the continuous fasting without interruption, the Prophet (sallallahu alayhi wa sallam) said as a warning that such a person neither receives the reward of fasting nor enjoys the pleasure of breaking the fast, meaning it is not permissible. The second case, which is fasting for two days and breaking the fast for one day, is also a burdensome and difficult practice. The third case also involves hardship, but the easiest and most complete in reward is to fast three days in every month, which is desirable and sought after.

➍ Although ‘Ashura refers to the tenth of Muharram, one should also fast a day before or after it. (Further details will come ahead in ahadith: 2442 and those that follow.)

➎ The expiation for the past year means that its shortcomings are forgiven, and the expiation for the coming year means that Allah will protect him from sins, or if they occur, He will forgive them. It should be noted that all such encouraging and motivating ahadith are conditional upon these righteous deeds being accepted by Allah the Exalted; only then will this reward be established... and who knows whether his deed has actually been accepted. Therefore, a believer cannot be deceived by performing good deeds. Rather, he strives for more righteous deeds in hope of acceptance and remains concerned that perhaps his deeds may be rejected.