Allah is the Arabic word for God used by both Arab Muslims and Arab Christians. The Bible in Arabic also uses the name Allah to refer to God. Muslims believe in the one Creator of the Universe, referring to Him as “Allah” which is the Arabic word for “God”. Muslims worldwide, even English-speaking Muslims, frequently use the Arabic word “Allah” because Arabic is the language of the Qur’an. But Allah is no different than the God of Abraham, Moses and Jesus. The Creator is the Creator regardless of what people call Him. In the English language He is most commonly referred to as “God”. Yet Jesus spoke a different language, referring to God as “Eloi” in Mark 15:34. Are “God” and “Eloi” different gods? Many Hispanics call God “Dios” and many French say “Dieu”. It would logically follow then that people who refer to God as “Allah” in the Arabic language are referring to the very same God. In fact, many Arab Jews and Arab Christians call God “Allah”. And the word “Allah” is written in Arabic script on the walls of many Arab churches and on the pages of Arabic Bibles. So while the understanding of God may differ between faith groups, the various names used to describe Him does not change the fact that the one Creator of the Universe is the God of all people.
your God is One God.
―Quran 2:163

This is the definition of Allah from Quran:
In the name of God, the Gracious, the Merciful.
1. Say, “He is God, the One.
2. God, the Absolute.
3. He begets not, nor was He begotten.
4. And there is nothing comparable to Him.”
-Surah Al-Ikhlas 112

"Allah" is the unique Arabic name of The One True God. Allah has no rivals, partners, equals, children or parents. He is not like His creation, as nothing shares His divine essence and perfect attributes. Some of His names and attributes include: The Creator, The Most Merciful, The Most High, The All-Powerful, The Most Just, The All-Wise, The Sustainer and The All-Knowing.

He is the Creator and Sustainer of all, the One who has granted us countless blessings, such as our faculties of hearing, seeing and thinking, as well as the ability to walk, talk and be productive. As such, we should acknowledge, thank and worship Him alone by following His guidance.

It is rational to conclude that such a complex and balanced universe is not possible by any other than a powerful and intelligent being. It is therefore illogical to believe that the universe created itself, or was the result of random or coincidental events.

وَلِلَّهِ الْأَسْمَاءُ الْحُسْنَىٰ فَادْعُوهُ بِهَا وَذَرُوا الَّذِينَ يُلْحِدُونَ فِي أَسْمَائِهِ سَيُجْزَوْنَ مَا كَانُوا يَعْمَلُونَ
Allah has the Most Beautiful Names. So call upon Him by them, and keep away from those who abuse His Names. They will be punished for what they used to do.
— Quran 7:180

this is a list of some Names of Allah:

The Creator الخالق
The Maker البارئ
The Giver of Life المحيي
The Bringer of Death المميت
The Most Compassionate الرؤوف
The Most Gracious الرحمن
The Most Merciful الرحيم
The All-Forgiving الغفور
The Almighty العزيز
The Most Kind البر
The Truth الحق
The King الملك
The Great الكبير
The Kind اللطيف
The Most Holy القدوس
The source of Peace السلام
The All-Knowing العليم
The All-Hearing السميع
The All-Seeing البصير
The Forbearer الحليم
The Majestic الجليل
The Generous الكريم
The Loving الودود
The Wise الحكيم
The All Glorious المجيد
The Ever Living الحي
The Everlasting الصمد
The Originator المبدئ
The Ever-Pardoning التواب
The Most Powerful القادر
The Magnificent الماجد
The Forgiver العفو
The Strong القوي
The One الواحد
The First الأول
The Light النور
The Guide الهادي
The Patron الوالي
The Owner of All Sovereignty مالك الملك
The Lord of Majesty and Generosity ذو الجلال و الإكرام
The Ever Enduring الباقي
The Equitable المقسط
The Patient الصبور
The Last الآخر

allah, art, and design image

via Islamic Pamphlets
http://www.islamicpamphlets.com/about-islam-brief-introduction