How does dhikr polish the heart?

Dhikr cleans the mirror of the heart to reflect the Divine light. As mentioned in the hadith, the Messenger of Allah ﷺ used to say, "There is a polish for everything and the polish for hearts is the remembrance of Allah." [Bayhaqi 2/254]

All souls are born on nature, fitrah, but slowly, steadily they are tainted by the world and its desires. The only salvation for that soul is the remembrance of Allah, until all doubts and delusions are annihilated and the soul becomes pure again.

It is through the dhikr of Allah that the heart is cleansed and the state of excellence, ihsan, is achieved, which is as in the Prophetic phrase, "as though you see Him." The food for the soul, the Ruh, is the remembrance of Allah.

It is through dhikr that faith is strengthened and the soul is elevated, and it was in this context that 'Umar ibn al-Khattab may Allah be pleased with him said, "If the Iman of Abu Bakr may Allah be pleased with him were weighed against the Iman of the entire Umma, it would outweigh it."