The Quran is the Word of Allah and an answer to the prayers of those who call upon Him for guidance. The first chapter of the Quran, Surah Al-Fatihah, also named The Opening, is a supplication to the Creator of the Heavens and the Earth, to keep us on the Straight Path.
There are numerous reasons why Muslim parents want their children to memorize the Quran. It is part of our tradition and a feat that sets us apart from other religious adherents.