Why these days are special
The Prophet Muhammad ﷺ said that no deeds on other days are better than good deeds in these ten days. His companions asked if this includes striving in the way of Allah. He said that it does, except for a person who went out putting his life and his wealth at risk and returned with nothing.
Many scholars of tafsir, including Ibn Abbas, also understand the "ten nights" in Quran 89:2 to mean these days. Quran 22:28 also speaks of remembering Allah on "known days", which many early scholars explained as these ten days. They include the day of Arafah, and they lead to the day of sacrifice.