Hifz means memorizing the holy Quran. There are lots of benefits given in the hadeeth for memorising the Quran.
When the holy Quran was revealed to the prophet Muhammed (sallallaahu 'alayhe wa sallam) it was revealed verse by verse (Ayah by Ayah). Sometimes many Ayah were revealed. The prophet would then ask recite the ayah to the Sahabah who would then either write or memorise.
