Short answer
Because Allah chose Friday as the special day of the Muslim week. The Prophet ﷺ said it is the best day the sun rises on: Adam was created on it, entered Paradise on it and left it on it, and the Hour will come on a Friday. Earlier communities were given Saturday and Sunday, and Muslims were guided to Friday.
Jumuah prayer is fard on resident adult men on Friday at Dhuhr time, established by the Quran, the sunnah and consensus. Friday is not a day of rest in Islam: Muslims leave trade for the prayer and may go back to work after it.
The four schools agree on this.
Explanation
Jumu'ah means "gathering". It is the day the Muslims of a town gather for the khutbah and the prayer, and a whole surah of the Quran, Surah al-Jumu'ah, is named after it. Allah commands believers to hurry to the remembrance of Allah when the call is made on that day.
The Prophet ﷺ explained why Friday is special:
- It is the best day on which the sun rises.
- Adam was created on it, entered Paradise on it and was sent out of it on it.
- The Hour will come on a Friday.
- It contains an hour in which du'a is answered.
He also said that Allah led the earlier communities away from Friday: the Jews were given Saturday and the Christians Sunday, and then Allah guided the Muslims to Friday. So Friday is the Muslim week's special day, but it is not a sabbath. After the prayer Allah says, "disperse within the land and seek from the bounty of Allah", so working on Friday outside the prayer time is fine. The four schools agree on all of this.
For what to do on Friday, see Friday in Islam and how to pray Jummah. Who must attend is covered in who has to pray Jummah.
The evidence
Quran, Surah Al-Jumu'a 62:9
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا نُودِىَ لِلصَّلَوٰةِ مِن يَوْمِ ٱلْجُمُعَةِ فَٱسْعَوْا۟ إِلَىٰ ذِكْرِ ٱللَّهِ وَذَرُوا۟ ٱلْبَيْعَ ۚ ذَٰلِكُمْ خَيْرٌۭ لَّكُمْ إِن كُنتُمْ تَعْلَمُونَ ﴿٩﴾
O you who have believed, when [the adhan] is called for the prayer on the day of Jumu'ah [Friday], then proceed to the remembrance of Allah and leave trade. That is better for you, if you only knew.
Friday's prayer is commanded by name in the Quran.
Quran, Surah Al-Jumu'a 62:10
فَإِذَا قُضِيَتِ ٱلصَّلَوٰةُ فَٱنتَشِرُوا۟ فِى ٱلْأَرْضِ وَٱبْتَغُوا۟ مِن فَضْلِ ٱللَّهِ وَٱذْكُرُوا۟ ٱللَّهَ كَثِيرًۭا لَّعَلَّكُمْ تُفْلِحُونَ ﴿١٠﴾
And when the prayer has been concluded, disperse within the land and seek from the bounty of Allah, and remember Allah often that you may succeed.
Friday is not a day of rest; work resumes after the prayer.
Sahih Muslim 854
Sahih... خير يوم طلعت عليه الشمس يوم الجمعة فيه خلق آدم ...
"The best day on which the sun rises is Friday; on it Adam was created."
Why Friday is the most virtuous day.
Sahih Muslim 856
Sahih... أضل الله عن الجمعة من كان قبلنا ...
"Allah led those before us away from Friday."
Muslims were guided to Friday, while earlier communities had Saturday and Sunday.
Where the ruling is recorded
- al-Hidaya, Kitab al-Salah, chapter on Jumuah. Jumuah is fard on resident, healthy adult men and is prayed in the time of Dhuhr.
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.