(The Most Sacred / The Most Holy)
The one who is clear of any imperfection, weakness, or shortcoming.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Quddus (in Arabic: ٱلْقُدُّوسُ), meaning the most pure or the most holy. He is so far removed from any imperfection and does not suffer from any shortcomings. The mere mention of being free from defects borders on insult as it implies the possibility of imperfection. He transcends all that we perceive as perfection, and all sublime attributes belong to Him.
From the root qaf-dal-sin (ق د س), which has the following classical Arabic connotations: to be pure, clean, spotless be far removed from impurity or imperfection to be holy, sacred, and hallowed.
The name Al-Quddus is derived from the word quds meaning sanctify, purify, or to be holy. Al-Quddus is the superlative which captures His essence of perfection. He is far removed from resembling anything. Imam al-Ghazali writes in his treatise of the 99 names, "the Holy is the one who transcends every one of the attributes of perfection which the majority of creatures thinks of as perfection."
The Holy Spirit:
The Qur'an mentions the concept of the Holy Spirit (Ruh Al-Quddus) four times. It is understood that He purifies and makes holy through this spirit. This is the concept of the divine force and influence Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has over His creatures. Whenever you see either Ruh al-Quddus or Ruh al-Amin (the faithful or trustworthy spirit, see 26:193 for example) the commentators of the Qur'an interpret it as being interchangeable with the Angel Jibrel.
In the tafsir of Ibn Kathir for Surah Maidah ayah 110, "O Isa, son of Maryam! Remember My favor to you and to your mother when I supported you with Ruh il-Qudus (Jibril) so that you spoke to the people in the cradle and in maturity [...] and you healed those born blind, and the lepers by My permission, and when you brought forth the dead by My permission;"
When Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ mentions the passing of this spirit it's understood as to cast a reflection of His divine characteristics on His creation. It makes a thing pure, and wholesome and removes any imperfections. Isa (as) was gifted with this quality making him infallible and enabled him to perform these miracles.
Tilkar Rusulu faddalnaa ba’dahum ‘alaa ba’d; minhum man kallamal laahu wa rafa’a ba’dahum darajaat; wa aatainaa ‘Eesab na Maryamal baiyinaati wa ayyadnaahu bi Roohil Qudus; wa law shaaa’al laahu maqtatalal lazeena mimba’dihim mim ba’di maa jaaa’athumul baiyinaatu wa laakinikh talafoo faminhum man aamana wa minhum man kafar; wa law shaaa’al laahu maq tataloo wa laakinnallaaha yaf’alu maa yureed (section 33)
"Those messengers – some of them We caused to exceed others. Among them were those to whom Allah spoke, and He raised some of them in degree. And We gave Jesus, the Son of Mary, clear proofs, and We supported him with the Pure Spirit. If Allah had willed, those [generations] succeeding them would not have fought each other after the clear proofs had come to them. But they differed, and some of them believed and some of them disbelieved. And if Allah had willed, they would not have fought each other, but Allah does what He intends." — (Qur'an 2:253)
Iz qaalal laahu yaa ‘Eesab-na-Maryamaz kur ni’matee ‘alaika wa ‘alaa waalidatika; iz aiyattuka bi Roohil Qudusi tukallimun naasa fil mahdi wa kahlanw wa iz ‘allamtukal kitaaba wal Hikmata wa Tawraata wal Injeela wa iz Takhluqu minat teeni kahai ‘atit tairi bi iznee fatanfukhu feeha fatakoonu tairam bi iznee wa tubri’ul akmaha wal abrasa bi iznee wa iz tukhrijul mawtaa bi iznee wa iz kafaftu Baneee Israaa’eela ‘anka iz ji’tahum bil baiyinaati fa qaalal lazeena kafaroo minhum in haazaaa illaa sihrum mubeen
[The Day] when Allah will say, “O Jesus, Son of Mary, remember My favor upon you and upon your mother when I supported you with the Pure Spirit and you spoke to the people in the cradle and in maturity; and [remember] when I taught you writing and wisdom and the Torah and the Gospel; and when you designed from clay [what was] like the form of a bird with My permission, then you breathed into it, and it became a bird with My permission; and you healed the blind and the leper with My permission; and when you brought forth the dead with My permission; and when I restrained the Children of Israel from [killing] you when you came to them with clear proofs and those who disbelieved among them said, 'This is not but obvious magic.'" — (Qur'an 5:110)
Qul nazzalahoo Roohul Qudusi mir Rabbika bilhaqqi liyusabbital lazeena aamanoo wa hudanw wa bushraa lilmuslimeen
"Say, [O Muhammad], 'The Pure Spirit has brought it down from your Lord in truth to make firm those who believe and as guidance and good tidings to the Muslims.'" — (Qur'an 16:102)
Huwal-laahul-lazee laaa Ilaaha illaa Huwal-Malikul Quddoosus-Salaamul Muminul Muhaiminul-aAzeezul Jabbaarul-Mutakabbir; Subhaanal laahi Ammaa yushrikoon
"He is Allah, other than whom there is no deity, the Sovereign, the Pure, the Perfection, the Bestower of Faith, the Overseer, the Exalted in Might, the Compeller, the Superior. Exalted is Allah above whatever they associate with Him." — (Qur'an 59:23)
Yusabbihu lilaahi maa fis samaawaati wa maa fil ardil Malikil Quddoosil ‘Azeezil Hakeem
"Whatever is in the heavens and whatever is on the earth is exalting Allah, the Sovereign, the Pure, the Exalted in Might, the Wise." — (Qur'an 62:1)
From the hadith, A'isha reported that the Messenger of Allah (ﷺ) "used to pronounce while bowing and prostrating himself: (subbuhun quddus rabb al-mala'ikati wal-ruh) All Glorious (سُبُّوحٌ), All Holy (قُدُّوسٌ), Lord of the Angels (رَبُّ الْمَلاَئِكَةِ) and the Spirit (وَالرُّوحِ)." 
Narrated Ubayy ibn Ka'b: When the Messenger of Allah (ﷺ) offered salutation in the witr prayer, he said: Glorify (سُبْحَانَ) be to the king (الْمَلِكِ) most holy (الْقُدُّوسِ). 
It was narrated from Ubayy bin Ka'b that: The Messenger of Allah (ﷺ) used to pray witr with three rak'ahs. In the first he would recite: "Glorify the Name of Your Lord, the Most High" in the second: "Say: O you disbelievers!", and in the third: "Say: He is Allah, (the) One". And he would say the Qunut before bowing, and when he finished he would say: Subhanal-Malikil-Quddus (Glory be to the Sovereign, the Most Holy) three times, elongating the words the last time. 
We can benefit from knowing Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Quddus by trying to be pure and sanctified. We need to cleanse ourselves where Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ looks, which is in our hearts and our actions. This is a lifelong journey of freeing ourselves from desires and avoiding anger, lust, and addictions to food or clothing. Instead, be engaged in tawbah, i.e., seek Allah's forgiveness, for He can cleanse you of any mistakes or wrongdoings. He can guide the one who is lost. As we'll explore in later sections, the name Al-Afuww, the effacer of sins - He pardons any sin and leaves no trace of any fault. Remember, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Quddus, the pure and the Holy, and He created you. There's a purpose and wisdom for your existence. We may not understand it or seem lost at times. But when we turn back to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ we become reoriented and start to feel whole.