Yes, it is permissible for believing men and women to read the Qur'aan even if they do not understand the meaning, but it is prescribed to ponder and think so that one may understand, and to refer to books of tafseer (commentaries) if one has enough knowledge to understand them, and to refer to books of tafseer and Arabic language in order to benefit from that, and he can ask scholars about anything he does not understand. What is meant is that he should ponder the meanings, because Allah says (interpretation of the meaning):
“(This is) a Book (the Qur’aan) which We have sent down to you, full of blessings, that they may ponder over its Verses, and that men of understanding may remember”
The believer should ponder the meanings, i.e., he should pay attention to reading and think about what it means; he should understand the meanings and thus he will benefit from it. If he does not understand the meaning perfectly, he will still understand many meanings. So let him read carefully and ponder and understand. This also applies to women. The reader should benefit from the words of his or her Lord and understand the meaning so that he may act upon it. Allah says (interpretation of the meaning):
“Do they not then think deeply in the Qur’aan, or are their hearts locked up (from understanding it)?”
Our Lord, may He be glorified and exalted, urges and encourages us to think and ponder His words. When the believer -- man or woman -- reads the Book of Allah, it is prescribed for them to ponder and think and pay attention to what is read, so that they may benefit from the words of Allah and so that they may understand the words of Allah and so that they may act upon what they learn from the words of Allah. They may seek help in doing so from books of tafseer that have been written by scholars such as those by Ibn Katheer, Ibn Jareer, al-Baghawi, al-Shawkaani and others. They may also make use of books of Arabic language and ask scholars who are known for their knowledge and virtue about anything they do not understand. End quote.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him).