(The Most Sacred / The Most Holy)
The One who is pure from any imperfection and clear from children and adversaries
For Allah is Al-Qaddus (in arabic: ٱلْقُدُّوسُ), so far removed of any imperfection. He has no shortcomings, evil is not attributed to Him. 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, it is inconceivable. All sublime attributes belong to Him.
From the root q-d-s which has the following classical Arabic connotations: to be pure, clean, spotless to be far removed from impurity or imperfection to be holy, sacred, hallowed.
In the Qur'an it mentions the concept of the Holy Spirit (Ruh al-Qaddus) four times. 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-Qaddus or Ruh al-Amin (the faitful or trustworthy spirit, see 26:193 for example) it's interpreted by scholars 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." 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, wholesome, and removes any imperfections. Isa (as) was gifted with this quality making him infallible.
"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." (2:253)
"[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."(5:110)
"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.'" (16:102)
"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."(59:23)
"Whatever is in the heavens and whatever is on the earth is exalting Allah, the Sovereign, the Pure, the Exalted in Might, the Wise."(62:1)
From the hadith, A'isha reported that the Messenger of Allah (ﷺ)"used to pronounce while bowing and prostrating himself: 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 al-Qaddus by trying to be pure and sanctified (i.e., to the best of our abilities). We need to cleanse ourselves where Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ looks, which is in our hearts and our actions. This is a life long journey trying to free ourselves from desires, refrain from anger, lust, addictions to food, and/or clothing (the material world).