It is a day on which the people of pre-Islamic days observed fast. So he who liked to fast on this day should do so, and he who liked to abandon it should abandon it. 'Abdullah (Allah be pleased with him) did not observe fast except when it coincided (with the days when he was in the habit of observing voluntary fasts during every month).  

أَنَّهُ سَمِعَ رَسُولَ اللَّهِ ﷺ يَقُولُ فِي يَوْمِ عَاشُورَاءَ إِنَّ هَذَا يَوْمٌ كَانَ يَصُومُهُ أَهْلُ الْجَاهِلِيَّةِ فَمَنْ أَحَبَّ أَنْ يَصُومَهُ فَلْيَصُمْهُ وَمَنْ أَحَبَّ أَنْ يَتْرُكَهُ فَلْيَتْرُكْهُ وَكَانَ عَبْدُ اللَّهِ ؓ لاَ يَصُومُهُ إِلاَّ أَنْ يُوَافِقَ صِيَامَهُ  

[Machine] The Messenger of Allah ﷺ said: "This is the day of Ashura, which the Quraysh used to fast during the time of ignorance. So whoever among you wishes to fast on this day, let them fast, and whoever wishes to abandon it, let them abandon it." Ibn Umar used to observe this fast except when it coincided with his own fast.  

قَالَ رَسُولُ اللَّهِ ﷺ «هَذَا يَوْمُ عَاشُورَاءَ كَانَتْ قُرَيْشٌ تَصُومُهُ فِي الْجَاهِلِيَّةِ فَمَنْ أَحَبَّ مِنْكُمْ أَنْ يَصُومَهُ فَلْيَصُمْهُ فَمَنْ أَحَبَّ مِنْكُمْ أَنْ يَتْرُكَهُ فَلْيَتْرُكْهُ» وَكَانَ ابْنُ عُمَرَ لَا يَصُومُهُ إِلَّا أَنْ يُوَافِقَ صِيَامَهُ  

It is a day on which the people of pre-Islamic days observed fast. So he who liked to fast on this day should do so, and he who liked to abandon it should abandon it. 'Abdullah (Allah be pleased with him) did not observe fast except when it coincided (with the days when he was in the habit of observing voluntary fasts during every month). (Using translation from Muslim 1126d)   

أَنَّهُ سَمَعَ رَسُولَ اللهِ ﷺ يَقُولُ فِي يَوْمِ عَاشُورَاءَ إِنَّ هَذَا يَوْمٌ كَانَ يَصُومُهُ أَهْلُ الْجَاهِلِيَّةِ فَمَنْ أَحَبَّ أَنْ يَصُومَهُ فَلْيَصُمْهُ وَمَنْ أَحَبَّ أَنْ يَتْرُكَهُ فَلْيَتْرُكْهُ وَكَانَ عَبْدُ اللهِ لَا يَصُومُهُ إِلَّا أَنْ يُوَافِقَ صِيَامَهُ  

"إِنَّ هذا يَوْمٌ كان يصومُه أهل الجاهليِة، فمن أَحبَّ أَن يصومَه فليصُمْه، ومن أَحب أَن يترُكه فليترُكه. يعنى يوم عاشوراءَ".