The Surah referred to as the "Heart of the Qur'an" is Surah Yasin (Chapter 36). This designation comes from a hadith attributed to the Prophet Muhammad (SAW): "Everything has a heart, and the heart of the Qur'an is Yasin" (reported by Tirmidhi and others, though scholars have discussed its chain of narration).
Surah Yasin contains 83 verses and covers several core themes of Islamic belief: the truth of prophethood and revelation, the signs of Allah's creative power in nature, the reality of death and resurrection, and the certainty of the Day of Judgement. It presents parables and arguments that reinforce the central messages of the entire Qur'an, which is one reason scholars explain why it is called its "heart" - it encapsulates the essence of the Qur'an's message in a concentrated form.
Surah Yasin is widely recited by Muslims, especially for the sick and dying, and is considered to bring blessings and mercy.
The other surahs listed serve different purposes: Al-Rahman (Chapter 55) is known as the "Bride of the Qur'an" and repeatedly asks "Which of the favours of your Lord will you deny?" Al-Naba (Chapter 78) deals with the Day of Resurrection. Al-Mulk (Chapter 67) discusses Allah's sovereignty and is known for its protective virtue in the grave.