As Salaamu Alaikum!
Memorizing the Holy Qur’an is one of the most important ways to preserve Allah’s message. The others are to publish and distribute the book, or the text on the Internet and to recite the parts that one knows to other people. Prophet Muhammad (Sallallahu Alaihi Wassallam) said:
‘The best amongst you is the one who learns the Qur'an and teaches it.’ (Narrated by Al-Bukhari).
Actually, most important of all is to live by the message it contains, so as to be a good example to others. Aishah (may Allah be pleased with her), when asked to describe the character of Prophet Muhammad (Sallallahu Alaihi Wassallam) described it as ‘the Qur’an’.
The reward for remembering the message it contains, living by its guidance, and passing it on to others, is great:
"We, when the water (of Noah's Flood) overflowed beyond its limits, carried you, in the floating (Ark), That We might make it a Message unto you, and that ears (that should hear the tale and) retain its memory should bear its (lessons) in remembrance. "
Surah 69 Verses 11 - 12
It is Allah who helps people memorize the Qur’an, as he said to the Prophet Muhammad (Sallallahu Alaihi Wassallam)
By degrees shall We teach thee to declare (the Message), so thou shalt not forget,
Except as God wills: For He knoweth what is manifest and what is hidden.
And We will make it easy for thee (to follow) the simple (Path).
Therefore give admonition in case the admonition profits (the hearer).
Surah 87 Verses 6 - 9
In the Qur’an, Allah criticizes those of the People of the Book who
… forget a good part of the message that was sent them …,:
But because of their breach of their covenant, We cursed them, and made their hearts grow hard; they change the words from their (right) places and forget a good part of the message that was sent them, nor wilt thou cease to find them- barring a few - ever bent on (new) deceits: but forgive them, and overlook (their misdeeds): for God loveth those who are kind.
Surah 5 Verse 13
Allah Subhanahu wa Ta'ala frequently calls the Qur’an aldhikr, which is usually translated as a ‘reminding’. Also, the quality of a true Muslim is taqwa, which is consciousness and awareness of God. Therefore, the Qur’an reminds those who read and recite it of Allah, His gifts and His commands, so that they stay on the right path, follow His guidance on how to live the best way in this world and for the Hereafter, and do not stray or get distracted by the life of this world.
There are some people in this world, who would like nothing better than that Muslims should forget the message, and that no one else should get to hear about it. In the Muslim lands of the former USSR, for example, mosques, scholars and books were all destroyed systematically to exterminate the message of Islam. Those Muslims who forgot the message and were intimidated or even convinced by the communists began to live like them, drinking alcohol and indulging in many of the other practices the Qur’an forbids, so that they became distinguishable only by their Muslim names.
Nonetheless, even in the absence of books, those who had memorized the Qur’an were still able to pass on the message and the guidance it contains to some of their children and other people. In this way Islam has survived even in these places. This is why people who memorize the Qur'an are known as the protectors of the Qur'an.
In the light of all this, memorizing the Qur’an helps remind the one who does it, and others to whom he passes it on, of the message and commands of Allah, in its original Arabic words, so this in itself should help him towards a reward in al-Jannah (paradise). The Prophet (Sallallahu Alaihi Wassallam) said:
‘Such a person as recites the Qur'an and masters it by heart, will be with the noble righteous scribes (in Heaven). And such a person as exerts himself to learn the Qur'an by heart, and recites it with great difficulty, will have a double reward.’ (Narrated by Al-Bukhari)
He may also gain rewards like that of those he has ‘reminded’ to stay on the right path, in the same way as the person mentioned in this hadith:
Allah's Apostle (Sallallahu Alaihi Wassallam) said:
‘He who introduces some good practice in Islam, which is followed after him (by people), will be assured of a reward like those who followed it, without their rewards being diminished in any respect.’ (Narrated by Muslim)
With Best Wishes