In short, there are three traits which, once they lodge in a person, cause Allah on the Day of Resurrection neither to speak to him, nor to look at him, nor to purify him, and for him there will be a painful punishment.
This hadith is an explicit proof that Allah speaks, exactly as affirmed by Ahl al-Sunnah wa-l-Jamaʿah: Allah speaks as He wills, with whatever He wills, and whenever He wills. Nothing can thwart Him and nothing is beyond His reach. His command, when He intends a thing, is only to say to it, “Be,” and it comes to be; “and nothing in the heavens or on the earth can frustrate Allah. Surely He is All-Knowing, All-Powerful.” The wording “Allah will not speak to them” therefore implies that He will indeed speak to others— and so it is.
The hadith also shows that Allah’s gaze is of two kinds. The first is the universal gaze: nothing whatsoever is hidden from His sight—exalted is He; He sees all things. The second is the specific gaze of mercy, and this is what is denied to those people in the hadith: Allah will not look at them with a look of mercy.
It further establishes that Allah alone grants purification, as He says, “But Allah purifies whom He wills.” Thus the One who purifies circumstances, persons, and deeds is the Lord of all creation.
I ask Allah, the Exalted, to make us and you among those whom their Lord has purified; indeed He is capable of all things.