The night of Miraj literally translates to the Night of Ascent. It refers to the incident of Isra, His journey from Masjid al-Haram in Mecca to the Masjid al-Aqsa in al-Quds and Miraj when the Prophet Muhammad (Peace be upon Him) was taken to the Heavens.
It comes a month before Ramadan so it is part of greater awareness and preparation for that upcoming month of daily fasting.
This physical and spiritual journey is remembered and celebrated each year - usually on the 27th day of Rajab, the seventh month in the Muslim calendar.
There are many narrates about Isra and Miraj in the sources of hadith and in the books of siyar and evidence.
According to the common points of the narrations in Bukhari and Muslim, the event is as follows:
One night, when the Messenger of Allah was in the Kaaba, in a place called Hijr or Hatim, - in some narrations while he was asleep, or in a state of sleep and wakefulness - Gabriel came; opened his chest, cleaned his heart, and stomach out with Zam Zam then filled with faith and wisdom.
Subsequently, he took Muhammad [Peace be upon Him] from the Masjid al-Haram in Mecca to the Masjid al Aqsa in Jerusalem. The mode of transportation used for this commute in the middle of the night was Buraq, a white mule like an animal.
When Rasul al-Akram performed two Rak'ahs at Masjid Al-Aqsa and went out, Angel Gabriel brought two cups one filled with milk and the other with wine.
When the messenger of Allah chose the cup filled with milk, Gabriel said, "You have chosen disposition", and then took the Prophet Muhammed and raised it up to the sky of the world.
On each of the skies (heavens), Prophet Muhammed respectively met with Adam, Jesus, Joseph, Idris, Aaron, and Moses prophets; finally, in the seventh heaven, in Beytülma'mur, He met with Abraham Prophet.
He was taken to Sidrat al-Muntaha, which is a lote tree in Jannah that marks the end of the seventh heaven. No being can cross this point. Muhammad (Peace be upon Him) was the only one allowed. Even Angel Gebrail did not accompany Him past this point.
Allah revealed to Muhammad [Peace be upon Him] that all Muslims were to pray 50 times a day. As Muhammad (Peace be upon Him) was going back, Musa (AS) told him that 50 prayers were too many so Muhammad [Peace be upon Him] requested Allah to reduce the number of prayers. Allah reduced the mandatory prayers to 45 but Musa (AS) still thought they were too many so eventually on Muhammad's (Peace be upon Him) request, Allah reduced the number of prayers to 5.
According to the narration, the last verses of Surat al-Baqara were revealed to Rasul al-Akram in Miraj and the good news was given that those who do not associate partner with Allah will be forgiven.
Islamic scholars recommend that the night of Miraj be spent with prayers and dhikrs, primarily prayer worship and reading Holy Qur'an.