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