What is the explanation of the hadith: "So he took me and covered me until I reached my limit, then he released me and said, 'Read!' I said, 'I am not a reader'"?

What you asked about is part of the Hadith about the beginning of revelation. The Prophet's saying, "I am not a reader," means: I do not know how to read. Al-Qastallani and Mirqat al-Mafatih explained the meaning of "Ghattani" (he embraced me strongly/pressed me) as: he squeezed me forcefully until I reached a state of exhaustion and hardship. Gabriel (peace be upon him) repeated this three times. The reason for the repetition and the pressing was to emphasize the Prophet's attention, to divert him from worldly matters, and to prepare his heart for what was to be revealed to him.