Specifically, what is the meaning of "Alif Lām Mīm"?

Imām Ibn al-Jawzī (d. 597/1201) summarized the scholars' opinions in his book "Zād al-Masīr" as follows:

1. It is from the "mutashābih" known only to Allāh, i.e. among the mysterious and symbolic elements in the Qurʾān. Abū Bakr al-Ṣiddīq (may Allāh be pleased with him) said, "In every Book of Allah, there is a secret, and the secret of Allāh in the Qurʾān is in the beginnings of the chapters." [Al-Shaʿbī, Abū Ṣāliḥ, and Ibn Zayd]
2. The meaning is: "I am Allāh, I know (all)": [Ibn Masʿūd; Saʿīd ibn Jubayr; Abū al-Ḍuḥā from Ibn ʿAbbās]
3. It is an oath (qasam). [Abū Ṣāliḥ from Ibn ʿAbbās; Khālid al-Ḥadhdhāʾ from ʿIkrimah]
4. They are letters from names. Those who hold this view have various opinions: (i) The "Alif" is from "Allāh", the "Lām" is from "Jibrīl" (Gabriel), and the "Mīm" is from "Muḥammad". [Ibn ʿAbbās] (ii) The "Alif" is from "Allāh", the "Lām" is from "Laṭīf" (the Subtle One), and the "Mīm" is from "Majīd" (the Glorious One). [Abū al-ʿĀliyah]
5. It is one of the names of the Qurʾān. [Mujāhid, al-Shaʿbī, Qatādah, Ibn Jurayj]