The Illuminator, The One who Reveals, The One Who Guides.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ call himself An-Noor (in Arabic: ٱلْنُّورُ), meaning The One who illuminates and reveals the divine light of all the worlds. His light illuminates the heart and provides clarity and guidance. Anyone who turns their back to the true light will be in darkness.
From the root nun-waw-ra (ن و ر), which has the following classical Arabic connotations: to give light, to illuminate, to fill with light, to clarify, to reveal, to make visible, to blossom, to be in bloom (revealed), to be flaming, blazing and apparent to the senses, to enlighten, give counsel, and give advice.
Allah's Light Described:
The light of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ as described in the hadith and Qur'an, Abu Musa reported: The Messenger of Allah ﷺ was standing amongst us and he told us five things. He said: Verily the Exalted and Mighty God does not sleep, and it does not befit Him to sleep. He lowers the scale and lifts it. The deeds in the night are taken up to Him before the deeds of the day, and the deeds of the day before the deeds of the night. His veil is the light. In the hadith narrated by Abu Bakr (instead of the word "light"), it is fire. If he withdraws it (the veil), the splendor of His countenance would consume His creation so far as His sight reaches. 
Musa (as) was the only Prophet to have spoken with Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, and in his conversation, He asked if he could see him, "And when Moses arrived at Our appointed time and his Lord spoke to him, he said, "My Lord, show me [Yourself] that I may look at You." [Allah] said, "You will not see Me, but look at the mountain; if it should remain in place, then you will see Me." But when his Lord appeared to the mountain, He rendered it level, and Moses fell unconscious. And when he awoke, he said, 'Exalted are You! I have repented to You, and I am the first of the believers.'" Qur'an 7:143 So we learn that Allah's light is too powerful to be witnessed, "Vision perceives Him not, but He perceives [all] vision; and He is the Subtle, the Acquainted." (Qur'an 6:103)
The Various Interpretations:
It may be obvious, but worth mentioning. When we say Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Nur (The Light), it is not meant in the literal sense. The light we see is created and is not eternal. It gets emitted, absorbed, reflected, and refracted. Most scholars agree for it to be a name and attribute of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ it must be understood by the consequence and the properties of light. Light illuminates, makes things visible, and shows the way through the darkness. This leads to many interpretations of the name An-Nur which we'll explore in detail.
The first understanding is through His ability to manifest creation. Darkness is the absence of light; when we have no light, what remains is darkness. Similarly, it can be said if something did not exist, it was hidden or unknown. Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has the power to make them visible or known by creating them. It may seem paradoxical, but the natural state of existence is nothingness. We cannot fathom what absolute nothingness is, but that's the state from which all things come - it's the origin. People mistakenly assume that life is just the arrangement of atoms and molecules, but who created the atoms and molecules? Who was responsible for its perfect, orderly arrangement? What keeps everything going and allows them to remain? The only logical conclusion to this question is Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. Without Him saying, kun fa-yakoon, "Be, and it is!" Qur'an 36:82, they would not be known.
A second interpretation is light manifests; it makes things that are hidden - visible. His light operates at many levels. There is nothing that can be hidden from Him. He is the Al-Baseer (All-Seeing) and As-Sami (All-Hearing). His light reveals, and nothing escapes His view. "And with Him are the keys of the unseen; none knows them except Him. And He knows what is on the land and in the sea. Not a leaf falls but that He knows it." (Qur'an 6:59)
He also illuminates mankind through His book and His Messengers (may peace be upon them). He's a guide to those lost. So, in this sense, He lights upon light. From the darkness of nonexistence to the light of existence, from unguided to guided.
yaaa Ahlal kitaabi qad jaaa’akum Rasoolunaa yubaiyinu lakum kaseeram mimmmaa kuntum tukhfoona minal Kitaabi wa ya’foo ‘an kaseer; qad jaaa’akum minal laahi noorunw wa Kitaabum Mubeen
"O People of the Scripture, there has come to you Our Messenger making clear to you much of what you used to conceal of the Scripture and overlooking much. There has come to you from Allah a light and a clear Book." — (Qur'an 5:15)
The Darkness Within:
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ describes Himself in verse 35 of Surah Nur as the "light of the heaven and the earth." Everything that comes from Him comes through His light. To contrast, Shaykh Tosun Bayrak mentions how "the light of faith eliminates the darknesses of infidelity and sin within and without, bringing us to the light of Truth and salvation and serenity. The devil, and one's own devil, the ego, are those who like to operate in darkness and enter dark houses they will not enter that Divine house, the heart illuminated by the light of Faith."
The darkness in the believer is their ego. It calls us to pursue pleasure and things prohibited to pull us from Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. We can bring light into our life and the world, by and large, through following the commandments of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. By keeping ties of kinship, spreading peace, oppressing evils, gift-giving, feeding friends and neighbors, praying salah, remembering Him in our prayers, giving zakat to the needy, being patient, practicing gratitude, respecting and upholding the rights of parents, children, and women. This is the guidance of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ which illuminates the hearts.
Allaahu noorus samaawaati wal ard; masalu noorihee kamishkaatin feehaa misbaah; almisbaahu fee zujaajatin azzujaajatu ka annahaa kawkabun durriyyuny yooqadu min shajaratim mubaarakatin zaitoonatil laa shariqiyyatinw wa laa gharbiyyatiny yakaadu zaituhaa yudeee’u wa law lam tamsashu naar; noorun ‘alaa noor; yahdil laahu linoorihee mai yashaaa’; wa yadribul laahul amsaala linnaas; wallaahu bikulli shai’in Aleem
"Allah is the Light of the heavens and the earth. The example of His light is like a niche within which is a lamp, the lamp is within glass, the glass as if it were a pearly [white] star lit from [the oil of] a blessed olive tree, neither of the east nor of the west, whose oil would almost glow even if untouched by fire. Light upon light. Allah guides to His light whom He wills. And Allah presents examples for the people, and Allah is Knowing of all things." — (Qur'an 24:35)
Supplication of Prophet Muhammad ﷺ:
We can ask Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ to bless us with His light just as Prophet Muhammad ﷺ taught the sahabah. 
Allaahummaj’al fee qalbee nooran, wa fee sam’ee nooran, wa an yamini nooran, wa an yasari nooran, wa fawqi nooran, wa tahti nooran, wa amami nooran, wa khalfi nooran, wa a'dhim lee nooran.
"O Allah, put light in my heart and light in my hearing and light on my right and light on my left and a light above me and a light under me and a light in front of me and a light behind me and make my light great."
Reflecting on your light:
Every person has a light that emanates from them. The intensity at which it shines is determined by their upright character and the righteousness of their deeds. Every good you do illuminates the path toward paradise, and every evil takes from it. The intention of the believer, then, should be to focus on ways in which their being is like a moth to a flame, attracting others because of their light and goodness.
(12) Yawma taral mu’mineena walmu’minaati yas’aa nooruhum baina aydeehim wa bi aymaanihim bushraakumul yawma jannaatun tajree min tahtihal anhaaru khaalideena feeha; zaalika huwal fawzul ‘azeem (13) Yawma yaqoolul munaafiqoona walmunaafiqaatu lil lazeena aamanu unzuroonaa naqtabis min noorikum qeelarji’oo waraaa’akum faltamisoo nooran faduriba bainahum bisooril lahoo baabun, baatinuhoo feehir rahmatu wa zaahiruhoo min qibalihi-‘azaab
"(12) On the Day you see the believing men and believing women, their light proceeding before them and on their right, [it will be said], “Your good tidings today are [of] gardens beneath which rivers flow, wherein you will abide eternally.” That is what is the great attainment. (13) On the [same] Day the hypocrite men and hypocrite women will say to those who believed, “Wait for us that we may acquire some of your light.” It will be said, “Go back behind you and seek light.” And a wall will be placed between them with a door, its interior containing mercy, but on the outside of it is torment." — (Qur'an 57:12-13)
Ask Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ for forgiveness and to increase your light so we don't suffer the fate of those who get left behind because their light was too weak. The du'a has been underlined below for your reference.
Yaaa ayyuhal lazeena aamanoo toobooo ilal laahi tawbatan nasoohan ‘asaa rabbukum any-yukaffira ‘ankum sayyi aatikum wa yudkhilakum jannaatin tajree min tahtihal anhaaru yawma laa yukhzil laahun nabiyya wallazeena aamanoo ma’ahoo nooruhum yas’aa baina aydeehim wa bi aymaanihim yaqooloona rabbanaaa atmim lanaa nooranaa waghfir lana innaka ‘alaa kulli shai’in qadeer
"O you who have believed, repent to Allah with sincere repentance. Perhaps your Lord will remove from you your misdeeds and admit you into gardens beneath which rivers flow [on] the Day when Allah will not disgrace the Prophet and those who believed with him. Their light will proceed before them and on their right; they will say, 'Our Lord, perfect for us our light and forgive us. Indeed, You are over all things competent.'" — (Qur'an 66:8)