Short answer
Jerusalem holds al-Masjid al-Aqsa, the first qibla of the Muslims, the destination of the Prophet's ﷺ Night Journey, and one of the three mosques he urged people to travel to. It is a land of many prophets, which Allah calls blessed.
Sunni scholars agree that al-Masjid al-Aqsa is the third holiest mosque in Islam after al-Masjid al-Haram and al-Masjid al-Nabawi, that prayer there carries extra reward, and that Muslims prayed toward it for about sixteen or seventeen months after the Hijrah.
The four schools agree on this.
Explanation
The first qibla. In Makkah and for about sixteen or seventeen months in Madinah, the Muslims prayed toward Bayt al-Maqdis (Jerusalem). Then Allah turned the qibla to the Kaaba (2:144). Al-Bara ibn Azib reports this in Sahih al-Bukhari.
The Night Journey. Allah took the Prophet ﷺ by night from al-Masjid al-Haram to al-Masjid al-Aqsa, "whose surroundings We have blessed" (17:1). There he led the prophets in prayer, and from there he rose through the heavens in the Mi'raj. See What is the difference between Isra and Mi'raj?
An ancient house of worship. Abu Dharr asked which mosque was first set on earth. The Prophet ﷺ said al-Masjid al-Haram, then al-Masjid al-Aqsa, forty years later. He also said a journey for worship should only be made to three mosques: the Masjid al-Haram, his own mosque and al-Aqsa.
The land of prophets. Ibrahim, Lut, Dawud, Sulayman, Zakariya, Yahya and Isa lived or preached in and around it. Muslims came to govern it in the caliphate of Umar, and Salahuddin regained it in 583 AH (1187 CE). For the buildings, see Al-Aqsa and the Dome of the Rock and Is the Dome of the Rock a mosque?; for Salahuddin, see his life.
The evidence
Quran, Surah Al-Israa 17:1
بِسْمِ ٱللَّهِ ٱلرَّحْمَٰنِ ٱلرَّحِيمِ سُبْحَٰنَ ٱلَّذِىٓ أَسْرَىٰ بِعَبْدِهِۦ لَيْلًۭا مِّنَ ٱلْمَسْجِدِ ٱلْحَرَامِ إِلَى ٱلْمَسْجِدِ ٱلْأَقْصَا ٱلَّذِى بَٰرَكْنَا حَوْلَهُۥ لِنُرِيَهُۥ مِنْ ءَايَٰتِنَآ ۚ إِنَّهُۥ هُوَ ٱلسَّمِيعُ ٱلْبَصِيرُ ﴿١﴾
Exalted is He who took His Servant by night from al-Masjid al-Haram to al-Masjid al-Aqsa, whose surroundings We have blessed, to show him of Our signs. Indeed, He is the Hearing, the Seeing.
The Night Journey and the blessing of the land.
Quran, Surah Al-Baqara 2:144
قَدْ نَرَىٰ تَقَلُّبَ وَجْهِكَ فِى ٱلسَّمَآءِ ۖ فَلَنُوَلِّيَنَّكَ قِبْلَةًۭ تَرْضَىٰهَا ۚ فَوَلِّ وَجْهَكَ شَطْرَ ٱلْمَسْجِدِ ٱلْحَرَامِ ۚ وَحَيْثُ مَا كُنتُمْ فَوَلُّوا۟ وُجُوهَكُمْ شَطْرَهُۥ ۗ وَإِنَّ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ لَيَعْلَمُونَ أَنَّهُ ٱلْحَقُّ مِن رَّبِّهِمْ ۗ وَمَا ٱللَّهُ بِغَٰفِلٍ عَمَّا يَعْمَلُونَ ﴿١٤٤﴾
We have certainly seen the turning of your face, [O Muhammad], toward the heaven, and We will surely turn you to a qiblah with which you will be pleased. So turn your face toward al-Masjid al-Haram. And wherever you [believers] are, turn your faces toward it [in prayer]. Indeed, those who have been given the Scripture well know that it is the truth from their Lord. And Allah is not unaware of what they do.
The change of qibla from Jerusalem to the Kaaba.
Sahih al-Bukhari 399
Sahih... صلى نحو بيت المقدس ستة عشر أو سبعة عشر شهرا ...
"He prayed toward Bayt al-Maqdis for sixteen or seventeen months."
Jerusalem was the first qibla.
Sahih al-Bukhari 3366
Sahih... أي مسجد وضع في الأرض أول ...
"Which mosque was first set on the earth?"
Al-Aqsa was the second mosque on earth, forty years after the Masjid al-Haram.
Sahih al-Bukhari 1189
Sahih... لا تشد الرحال إلا إلى ثلاثة مساجد ...
"Do not set out on a journey except to three mosques."
Al-Aqsa is one of the three special mosques.
Where the ruling is recorded
- Fath al-Bari (Ibn Hajar), Commentary on Kitab al-Salat, chapter on facing the qibla, the change of qibla. Explains the reports of sixteen or seventeen months.
- al-Bidaya wa al-Nihaya (Ibn Kathir), Events of the years 15 to 16 AH, the conquest of Bayt al-Maqdis. Umar's coming to Jerusalem.
- al-Uns al-Jalil bi Tarikh al-Quds wa al-Khalil (Mujir al-Din), Section on the virtues of Bayt al-Maqdis. Classical history of Jerusalem and its virtues.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.