The term for marriage in the Quran is النِّكَاحِ (l-nikāḥ), the tri-lateral root for this word is ن ك ح and has the following derivative meanings.
ن ك ح = marriage, contract, tie a knot, cement, age of sexual maturity, age where one can sign a contract independently without a guardian.
All these terms provide us insight to what marriage is according to the Quran.
Marriage as a contract
An umbrella rule in the Quran is that all transactions must be mutually acceptable, therefore a marriage must be mutually acceptable to both parties, meaning one party cannot be forced into a marriage unwillingly.
[4:29] O you who believe, do not consume each others’ properties illicitly— only mutually acceptable transactions are permitted. You shall not kill yourselves. GOD is Merciful towards you.
يَاأَيُّهَا الَّذِينَ آمَنُوا لَا تَأْكُلُوا أَمْوَالَكُمْ بَيْنَكُمْ بِالْبَاطِلِ إِلَّا أَنْ تَكُونَ تِجَارَةً عَنْ تَرَاضٍ مِنْكُمْ وَلَا تَقْتُلُوا أَنْفُسَكُمْ إِنَّ اللَّهَ كَانَ بِكُمْ رَحِيمًا
As part of a marriage contract, the husband and wife must also mutually agree upon a dowry which the husband will provide to the wife during the engagement process (2:236-237; 4:24-25).
Tieing a knot
The expression to tie a knot means to finalize a contract. In the case of marriage the final step of marriage is consummation where the couple seal their vows through intercourse (2:235), after the husband makes a solemn pledge to the wife (4:21).
When cement is dried it is permanently bonded together, similarly when two individuals are married the intention is that couple’s intention is to be together forever. Obviously that is not always the case, note the concept of divorce, but if the marriage is conducted with an expectation of divorce then this would be a form of prostitution as is done in some Islamic countries under the guise of “temporary marriages” or “nikah mut’ah.”
This is the reason God hates divorce, because in a divorce we are breaking our commitments that we made God a guarantor over.
[16:91] You shall fulfill your covenant with GOD when you make such a covenant. You shall not violate the oaths after swearing (by God) to carry them out, for you have made GOD a guarantor for you. GOD knows everything you do.
وَأَوْفُوا بِعَهْدِ اللَّهِ إِذَا عَاهَدْتُمْ وَلَا تَنْقُضُوا الْأَيْمَانَ بَعْدَ تَوْكِيدِهَا وَقَدْ جَعَلْتُمُ اللَّهَ عَلَيْكُمْ كَفِيلًا إِنَّ اللَّهَ يَعْلَمُ مَا تَفْعَلُونَ
Additionally, in the following verse God uses the term صِهْرًا (ṣih’ran) in reference to marriage.
[25:54] He is the One who created from water a human being, then made him reproduce through marriage and mating. Your Lord is Omnipotent.
وَهُوَ الَّذِي خَلَقَ مِنَ الْمَاءِ بَشَرًا فَجَعَلَهُ نَسَبًا وَصِهْرًا وَكَانَ رَبُّكَ قَدِيرًا
This word has the same meaning in Arabic as in English as into sear, but in Arabic this word also has the meaning to melt or liquify. I believe the reason this expression is used towards marriage in this verse is because when two people are married and, if God wills, reproduce they are joining in a life long union that is locked in biology through their future offspring.
Age of sexual maturity
In order to be able to marry both the husband and wife need to be sexually mature. We see the word النِّكَاحَ (l-nikāḥa) for marriage used in this context in the following verse:
[4:6] You shall test the orphans when they reach puberty. As soon as you find them mature enough, give them their property. Do not consume it extravagantly in a hurry, before they grow up. The rich guardian shall not charge any wage, but the poor guardian may charge equitably. When you give them their properties, you shall have witnesses. GOD suffices as Reckoner.
وَابْتَلُوا الْيَتَامَىٰ حَتَّىٰ إِذَا بَلَغُوا النِّكَاحَ فَإِنْ آنَسْتُمْ مِنْهُمْ رُشْدًا فَادْفَعُوا إِلَيْهِمْ أَمْوَالَهُمْ وَلَا تَأْكُلُوهَا إِسْرَافًا وَبِدَارًا أَنْ يَكْبَرُوا وَمَنْ كَانَ غَنِيًّا فَلْيَسْتَعْفِفْ وَمَنْ كَانَ فَقِيرًا فَلْيَأْكُلْ بِالْمَعْرُوفِ فَإِذَا دَفَعْتُمْ إِلَيْهِمْ أَمْوَالَهُمْ فَأَشْهِدُوا عَلَيْهِمْ وَكَفَىٰ بِاللَّهِ حَسِيبًا
In this verse God is informing us that an orphan needs to be sexually mature before they are able to have control over their property. One of the most precious properties we each have is the decisions of our own body which is essential in order to be able to commit to a marriage.
Age where one can independently sign a contract
The same verse above also informs us that the age one can marry is also the age where one can independently sign a contract. As marriage is a contract, it requires both parties to be both sexually mature and mentally mature in order to be able to sign a contract on their own without a guardian.