Arabic Root:
From the root mim-jim-dal (م ج د), which has the following classical Arabic connotations: to be glorious, dignified, majestic, noble, honorable, to be lauded, exalted, sublime, to be liberal, bountiful, and/or exceedingly generous.

Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Majeed meaning The All-Glorious One. His excellence is unparalleled as it does not resemble anything else. It is unique and alone. To be all-glorious is not a single standalone attribute but the quality of perfection of several attributes together (similar to how we discuss in the name Al-Jaleel - The Majestic One). Imam Al-Ghazali writes, "Al-Majid the All-Glorious is one who is noble in essence, beautiful in actions, and bountiful in gifts and in favours." In Ahmad Zarruq's book The Loftiest Goal in Elucidating Allah's Most Beautiful Names, he writes, "Al-Majīd comes from al-majd, namely, the furthermost limit of nobility which allows for no additional increase of such quality beyond it, since it is complete in itself and outwardly manifest."

In the Qur'an, it refers to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as Al-Majeed once, and it is beautifully paired with the name Al-Hamid ("The Praiseworthy"). After all, the one worthy of praise should be the one whose essence is excellence and nobility.

قَالُوٓاْ أَتَعۡجَبِينَ مِنۡ أَمۡرِ ٱللَّهِۖ رَحۡمَتُ ٱللَّهِ وَبَرَكَٰتُهُۥ عَلَيۡكُمۡ أَهۡلَ ٱلۡبَيۡتِۚ إِنَّهُۥ حَمِيدٞ مَّجِيدٞ

Qaalooo ata'jabeena min amril laahi rahmatul laahi wa barakaatuhoo alaikum Ahlal Bayt; innahoo Hameedun Majeed

English Translation:
"They said, 'Are you amazed at the decree of Allah? May the mercy of Allah and His blessings be upon you, people of the house. Indeed, He is Praiseworthy and Honorable.'"— (Qur'an 11:73)

ذُو ٱلۡعَرۡشِ ٱلۡمَجِيدُ

Zul Arshil Majeed

English Translation:
"Honorable Owner of the Throne,"— (Qur'an 85:15)

Now, as the word Majeed is used to describe both the Qur'an and the throne as glorious, it has been perfected and should be viewed with high status and ranking. The Qur'an is a glorious book since it serves as guidance for all of humanity. Of His throne, it is said, "His throne extends over the heavens and the Earth" (Qur'an 2:255)

قٓۚ وَٱلۡقُرۡءَانِ ٱلۡمَجِيدِ

Qaaaf; wal Qur aanil Majeed

English Translation:
"Qaf. By the honored Qur’an…"— (Qur'an 50:1)

From Hadith Literature:
Ibn Abi Laila reported: Ka'b b. 'Ujra met me and said: Should I not offer you a present (and added): The Messenger of Allah (ﷺ) came to us and we said: We have learned how to invoke peace upon you; (kindly tell us) how we should bless you. He (the Holy Prophet) said: Say: "O Allah: bless Muhammad and his family as Thou didst bless the family of Ibrahim. Verily Thou art (حَمِيدٌ - hamid) Praiseworthy and (مَجِيدٌ - majeed) Glorious, O Allah." ^[1]

Reflection:
The believer benefits in knowing Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Majeed in two ways. The first is in worship. Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ holds all honor and glory, our success is through Allah. Seek His pleasure by sincere and honest devotion to Him. When we recite durood Ibrahim in our salah, we call on the names Al-Hameed and Al-Majeed. He is the one worthy of praise because of the name Al-Majeed, i.e., the perfection of all attributes.

اللَّهُمَّ صَلِّ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ كَمَا صَلَّيْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ إِنَّكَ حَمِيدٌ مَجِيدٌ اللَّهُمَّ بَارِكْ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ كَمَا بَارَكْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ إِنَّكَ حَمِيدٌ مَجِيدٌ

Allahumma Salli ‘ala Muhammadin wa ‘ala aali Muhammadin, kama sallaita ‘ala Ibrahima wa ‘ala aali Ibrahima innaka Hamidum-Majeed. Allahumma barik ‘ala Muhammadin wa ‘ala aali Muhammadin kama barakta ‘ala Ibrahima wa ‘ala aali Ibrahima innaka Hameedum-Majeed. ^[2]

The second way a believer benefits from learning about Al-Majeed is by understanding that we should work on perfecting our attributes to raise our rank and increase our essence. To be a well-rounded Muslim means to work on our piety, devotion to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, studiousness, affection, kindness, generosity, etc. And to recoil from hypocrisy, falsehoods, and arrogance.

References:
01) Sahih Muslim 406a
02) Sahih al-Bukhari 3370