The address here is to the nation of the Prophet (saws). That is to say, We have sent you a messenger born and raised among you. He grew up with you. You have known his sincerity, honesty and integrity. He speaks your language, an Arabic messenger with a clear Arabic tongue.
(يَتْلُو عَلَيْكُمْ آيَاتِنَا) )reciting to you Our verses(: He conveys the Qur’an to you by reciting it.
(وَيُزَكِّيكُمْ) )and purifying you(: He purifies you from abomination, from idolatry, female infanticide, eating haram, drinking alcohol, injustice and aggression.
(وَيُعَلِّمُكُمُ الْكِتَابَ وَالْحِكْمَةَ) (and teaching you the Book and wisdom): There is a recitation of the book, and here is teaching of the book and wisdom, which is the Sunnah of the Prophet (saws), as Allah (swt) said:
{وَاذْكُرْنَ مَا يُتْلَىٰ فِي بُيُوتِكُنَّ مِنْ آيَاتِ اللَّهِ وَالْحِكْمَةِ ۚ}
(And remember what is recited in your houses of the verses of Allah and wisdom) (Al-Ahzaab:34)