Qadr or Qadar (Arabic: قدر), it means "fate or predestination or measure", and when used in relation to Allah (Glory be to Him), means Al-Qadar is Allah’s predestination of measurements and sustenance of everything and everyone, according to His Knowledge and Wisdom. 
A Muslim believes in Allah's predestination of all things and events (Qadhaa), His decree (Qadar), His wisdom in His actions, and His will. Nothing in the universe can occur, even the voluntary actions of His slaves, except after Allah's knowledge, and His decree of that event. A Muslim further believes that Allah (Glory be to Him)is Just in His predestination and His decree, Wise in all of His actions. His wisdom follows His will: Whatever He wills is, and whatever He does not will is not. There is no power or any movement except by Allah’s (Glory be to Him) will.
It is one of the six pillars of Eeman (faith) in Islam. It is divine destiny in Islam. More precisely, Qadr relates to the Destiny or fate about all events. Islamic theology claims that Omniscience of Allah (Glory be to Him) is not rationally inconsistent with the notion of free will granted to man in his earthly life. It’s a belief in predestination. The core Islamic belief is that man has been given free will in this life, and the retribution in the Hereafter life is based on how he utilizes his freedom of choice in the worldly trial.
Verily, We have created all things with Qadar (Divine Preordainments of all things before their creation, as written in the Book of Decrees Al-Lauh Al-Mahfûz). Qur'an.Surah Qamar 54:49
And there is not a thing, but with Us are the stores thereof. And We send it not down except in a known measure. Qur'an.Surah Hijr 15:21
No calamity befalls on the earth or in yourselves but is inscribed in the Book of Decrees (Al-Lauh Al-Mahfûz), before We bring it into existence. Verily, that is easy for Allah. Qur'an.Surah Hadeed 57:22.
No calamity befalls, but with the Leave [i.e. decision and Qadar (Divine Preordainments)] of Allâh, and whosoever believes in Allâh, He guides his heart [to the true Faith with certainty, i.e. what has befallen him was already written for him by Allâh from the Qadar (Divine Preordainments)], and Allâh is the All-Knower of everything. Qur'an.Surah Taghabun 64:11.
And with Him are the keys of the Ghaib (all that is hidden), none knows them but He. And He knows whatever there is in (or on) the earth and in the sea; not a leaf falls, but he knows it. There is not a grain in the darkness of the earth nor anything fresh or dry, but is written in a Clear Record. Qur'an.Surah Anam 6:59. 
Narrated Abu Huraira(R): Allah's Apostle (May Allah honour Him and grant Him Peace) said, "Adam and Moses argued with each other. Moses said to Adam, 'You are Adam whose mistake expelled you from Paradise.' Adam said to him, 'You are Moses whom Allah selected as His Messenger and as the one to whom He spoke directly; yet you blame me for a thing which had already been written in my fate before my creation?' "Allah's Apostle (May Allah honour Him and grant Him Peace) said twice, "So, Adam overpowered Moses." Sahih Al Bukhari Vol 4:621 
The Growth Of A Child In The Womb Of A Mother And His Destiny In Regard To His Livelihood, His Deeds, Both Good And Evil
Abdullah ibn Mas'ud reported that Allah's Messenger (May Allah honour Him and grant Him Peace) who is the most truthful (of the human beings) and his being truthful (is a fact) said: Verily your creation is on this wise. The constituents of one of you are collected for forty days in his mother's womb in the form of blood, after which it becomes a clot of blood in another period of forty days. Then it becomes a lump of flesh and forty days later Allah sends His angel to it with instructions concerning four things, so the angel writes down his livelihood, his death, his deeds, his fortune and misfortune. By Him, besides Whom there is no god, that one amongst you acts like the people deserving Paradise until between him and Paradise there remains but the distance of a cubit, when suddenly the writing of destiny overcomes him and he begins to act like the denizens of Hell and thus enters Hell, and another one acts in the way of the denizens of Hell, until there remains between him and Hell a distance of a cubit that the writing of destiny overcomes him and then he begins to act like the people of Paradise and enters Paradise.Sahih Al Muslim 6390
Al-Qadar encompasses four themes:
1) Allah’s Knowledge (al-'ilm),
2) Allah’s Writing (al-kitabah),
3) Allah’s Will (al-mashee’ah, and
4) Allah’s Creation (al-khalq).
Each of these themes is discussed below.
1. Knowledge - The belief that Allah’s knowledge encompasses everything, every matter, major or minor, and the time frame of everything that happens in this universe. Allah’s Knowledge encompasses all of His actions and actions taken by His slaves. "Verily Allah is the All-knowing of everything" Qur'an.surah Anfal 8:75
2. Pre-Recording - The belief that Allah recorded everything in a Tablet that He kept with Himself, called 'Al-Lawh Al-Mahfooth' (The Preserved Tablet). Allah Says ((what means)): “Do you not know that Allah knows what is in the heaven and earth? Indeed that is in a Record [i.e., Al-Lawh Al-Mahfooth]. Indeed that, for Allah, is easy.” Qur’an.Surah Hajj 22:70
Abdullaah bin 'Amr bin Al-'Aas® said that he heard the Messenger of Allah (May Allah honour Him and grant Him Peace) say: “Allah recorded the measurement of all matters pertaining to creation fifty thousand years before He created the heavens and earth.” [Muslim]
3. The Will of Allah - The belief that nothing, whether related to Allah’s actions or actions taken by His slaves, can occur without His permission. Allah Says (what means): “And your Lord creates what He wills and chooses...” [Qur’an.Surah Qasas 28:68] And (what means): “…And Allah does what He wills.” [Qur’an.Surah Ibrahim 14:27] And (what means) “It is He who forms you in the wombs however He wills…” [Qur’an.Surah Ale Imran 3:6] As for actions taken by His creation, Allah Says (what means): “…And if Allah had willed, He could have given them power over you, and they would have fought you.” [Qur’an.Surah Nisa 4:90] And (what means): “…And if Allah had willed, they would not have done so. So leave them and that which they invent.” Qur’an.Surah Anam 6:137. "If Allah willed, He would have made you one nation, but that (He) may test you in what He has given you." Qur'an.Surah Maidah 5:48
4. Creation - The belief that Allah created all creation, all what they possess of attributes, and all their actions. Allah Says (what means): “Allah is the Creator of all things, and He is, over all things, Disposer of affairs.” Qur’an.Surah Zumar 39:62
And (what means): “…He has created each thing and determined it with [precise] determination.” Qur’an.Surah Furqan25:2
Also, Ibraaheem said to his people (what means): “While Allah created you and that which you do?” Qur’an.Surah Saffath 37:96
Ali Ibn Abu Taalib narrated that the Prophet (May Allah honour Him and grant Him Peace) said: “The final destination, in Hell or Paradise, is already determined for each one of you.” A man said: “Should we depend on this fact, O Messenger of Allah?" (Meaning, to abandon doing good deeds) He said: “No! Perform (good) deeds, because everyone will be helped (to go on the path that he chooses and reach his destiny).” Then he read the ayath (which means): “As for he who gives [in charity] and fears Allah.” Qur’an.Surah Layl 92:5
It was reported that a man who was caught stealing was brought to 'Umar Ibn Al-Khattaab who ordered that this man’s hand be cut off. The man said: “Wait, O leader of the believers! I only stole because this was in the Qadr of Allah." 'Umar(R) replied “And we are amputating your hand because it is in the Qadr of Allah.” Source: A Translation of Sharh Usool Al-Eeman, by Shaykh Muhammad bin Saalih Al-Uthaymeen