Quran memorization is known as Hifz. It means to look out and learn the Quran both accurately and symbolically. Hifz is a method in which both knowledge and training are done verbally.
It is probably one of the best ways to strengthen the relationship between an individual and Allah. Memorizing the Quran helps us to heal physically, morally, and spiritually.
The Quran reminds us of our purpose of creation and aspires us to become a better version of ourselves. Familiarizing oneself with it has infinite benefits in this world and hereafter.
During the time of the Prophet (Peace Be upon Him), writing was an uncommon style of storing important matters and information; Thus memorization and oral transmission were the most effective methods of preserving information. This is how Quran memorization came into being. The Prophet PBUH would recite each verse and his companions would learn those verses by heart.