Arabic Root:
From the root qaf-ha-ra (ق ه ر), which has the following classical Arabic connotations: to overcome, conquer to overpower, master to dominate over, prevail to subdue, subjugate, to compel against one’s wishes.

The names Al-Qahhar and Al-Qahir:
There are two names, Al-Qahir, and Al-Qahhar. The name Al-Qahir is the base form meaning "the irresistible." On the other hand, Al-Qahhar is more emphatic, the one who is all over-powering, all-prevailing. Al-Qahir is mentioned twice in the Qur'an in Surah al-An'am verse 18 and verse 61. while Al-Qahhar is used more intensively, mentioned a total of 6 times.

This name informs us that Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ strength is unmatched. He has absolute sovereignty over all His creation. He is the dominator. Whoever is an enemy or challenges Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ stands no chance. He can humiliate them with ease. Things are measured on the scale of eternity, so if a person opposes Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ they will lose inevitably. There isn't a single creation that isn't subjected to Allah's will or could escape it.

The pairing of Al-Qahhar with Al-Wahid:
In the Qur'an, this name is also always coupled with the name Al-Wahid, meaning "The One." A king in this world can be powerful, but it's not because he possesses intrinsic power. It often comes with the buy-in of the state citizens or having a large army. If they were to turn on him, he would have no power. So this pairing of names shows the difference, He is one with complete dominion over all. We again see how the holistic approach of studying the names in their pairs brings light to a new meaning that we otherwise might've missed.

قُلۡ إِنَّمَآ أَنَا۠ مُنذِرٞۖ وَمَا مِنۡ إِلَٰهٍ إِلَّا ٱللَّهُ ٱلۡوَٰحِدُ ٱلۡقَهَّارُ

Qul innamaaa ana munzirunw wa maa min laahin illal laahul Waahidul Qahhaar

English Translation:
"Say, [O Muhammad], 'I am only a warner, and there is not any deity except Allah, the One, the Prevailing.'"— (Qur'an 38:65)

يَٰصَٰحِبَيِ ٱلسِّجۡنِ ءَأَرۡبَابٞ مُّتَفَرِّقُونَ خَيۡرٌ أَمِ ٱللَّهُ ٱلۡوَٰحِدُ ٱلۡقَهَّارُ

Yaa saahibayis sijni ‘a-arbaabum mutafarriqoona khayrun amil laahul waahidul qahhaar

English Translation:
"O [my] two companions of prison, are separate lords better or Allah, the One, the Prevailing?"— (Qur'an 12:39)

قُلۡ مَن رَّبُّ ٱلسَّمَٰوَٰتِ وَٱلۡأَرۡضِ قُلِ ٱللَّهُۚ قُلۡ أَفَٱتَّخَذۡتُم مِّن دُونِهِۦٓ أَوۡلِيَآءَ لَا يَمۡلِكُونَ لِأَنفُسِهِمۡ نَفۡعٗا وَلَا ضَرّٗاۚ قُلۡ هَلۡ يَسۡتَوِي ٱلۡأَعۡمَىٰ وَٱلۡبَصِيرُ أَمۡ هَلۡ تَسۡتَوِي ٱلظُّلُمَٰتُ وَٱلنُّورُۗ أَمۡ جَعَلُواْ لِلَّهِ شُرَكَآءَ خَلَقُواْ كَخَلۡقِهِۦ فَتَشَٰبَهَ ٱلۡخَلۡقُ عَلَيۡهِمۡۚ قُلِ ٱللَّهُ خَٰلِقُ كُلِّ شَيۡءٖ وَهُوَ ٱلۡوَٰحِدُ ٱلۡقَهَّـٰرُ

Qul mar Rabbus samaawaati wal ard; qulillaah; qul afattakhaztum min dooniheee awliyaaa’a laa yamlikoona li anfusihim naf’anw wa laa darraa; qul hal yastawil a’maa wal baseeru am hal tastawiz zulumaatu wannoor; am ja’aloo lillaahi shurakaaa’a khalaqoo kakhalqihee fatashaa bahal khalqu ‘alaihim; qulil laahu Khaaliqu kulli shai’inw wa Huwal Waahidul Qahhar

English Translation:
Say, “Who is Lord of the heavens and earth?” Say, “Allah.” Say, “Have you then taken besides Him allies not possessing [even] for themselves any benefit or any harm?” Say, “Is the blind equivalent to the seeing? Or is darkness equivalent to light? Or have they attributed to Allah partners who created like His creation so that the creation [of each] seemed similar to them?” Say, “Allah is the Creator of all things, and He is the One, the Prevailing.”— (Qur'an 13:16)

يَوۡمَ تُبَدَّلُ ٱلۡأَرۡضُ غَيۡرَ ٱلۡأَرۡضِ وَٱلسَّمَٰوَٰتُۖ وَبَرَزُواْ لِلَّهِ ٱلۡوَٰحِدِ ٱلۡقَهَّارِ

Yawma tubaddalul ardu ghairal ardi wassamaawaatu wa barazoo lillaahil Waahidil Qahhaar

English Translation:
"[It will be] on the Day the earth will be replaced by another earth, and the heavens [as well], and all creatures will come out before Allah, the One, the Prevailing."— (Qur'an 14:48)

لَّوۡ أَرَادَ ٱللَّهُ أَن يَتَّخِذَ وَلَدٗا لَّٱصۡطَفَىٰ مِمَّا يَخۡلُقُ مَا يَشَآءُۚ سُبۡحَٰنَهُۥۖ هُوَ ٱللَّهُ ٱلۡوَٰحِدُ ٱلۡقَهَّارُ

Law araadal laahu aiyattakhiza waladal lastafaa mimmaa yakhluqu maa yashaaa’; Subhaanahoo Huwal laahul Waahidul Qahhaar

English Translation:
"If Allah had intended to take a son, He could have chosen from what He creates whatever He willed. Exalted is He; He is Allah, the One, the Prevailing."— (Qur'an 39:4)

يَوۡمَ هُم بَٰرِزُونَۖ لَا يَخۡفَىٰ عَلَى ٱللَّهِ مِنۡهُمۡ شَيۡءٞۚ لِّمَنِ ٱلۡمُلۡكُ ٱلۡيَوۡمَۖ لِلَّهِ ٱلۡوَٰحِدِ ٱلۡقَهَّارِ

Yawma hum baarizoona laa yakhfaa alal laahi minhum shai; limanil mulkul Yawma lillaahil Waahidil Qahaar

English Translation:
"The Day they come forth nothing concerning them will be concealed from Allah. To whom belongs [all] sovereignty this Day? To Allah, the One, the Prevailing."— (Qur'an 40:16)

Reflection:
In using this beautiful name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ in your supplication, you can have the assurance that the most powerful is with you. If Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is with you, just as He was with Prophet Musa (as) when he stood against Firawn, or when Prophet Muhammad ﷺ was being persecuted by the Meccans, or when Prophet Dawud (as) fought and won the battle against Jalut, then nothing can overpower you. "If Allah should aid you, no one can overcome you" (Qur'an 3:160)

Du'a with this name:

لا إِلـهَ إِلاّ اللهُ الـواحِدُ القَهّـار رَبُّ السَّـمواتِ وَالأرْضِ وَما بَيْـنَهـما العَزيـزُ الغَـفّار

La ilaha illallah al-Wahidul-Qahhar, Rabbus-samawati wa ‘l-ardi wa ma baynahuma al-`Azīzul-Ghaffar.

English Translation:
“There is none worthy of worship but Allah, the One, the Victorious, Lord of the heavens and the earth and all that is between them, the All-Mighty, the All-Forgiving.”

References:
01) Hisn al-Muslim 112