Musa arrived in Midian as a fugitive after leaving Egypt, and found a group of shepherds watering their flocks at a well, with two women holding back, waiting for the crowd to clear. He watered their flock for them, then withdrew to the shade and prayed for Allah's provision. One of the two women, Shu'aib's daughter, was sent by her father to bring Musa to their home.

Shu'aib then offered Musa marriage to one of his daughters directly: "I wish to marry one of these two daughters of mine to you, provided that you stay in my service for eight years. If you complete ten, it will be a favour from you, but I do not wish to make it difficult for you. Allah willing, you will find me an agreeable man" (Surah Al-Qasas 28:27). Musa accepted, and this marriage is how Shu'aib's daughter became both a Prophet's daughter and a Prophet's wife.
قَالَ إِنِّي أُرِيدُ أَنْ أُنكِحَكَ إِحْدَى ابْنَتَيَّ هَاتَيْنِ عَلَىٰ أَن تَأْجُرَنِي ثَمَانِيَ حِجَجٍ ۖ فَإِنْ أَتْمَمْتَ عَشْرًا فَمِنْ عِندِكَ ۖ وَمَا أُرِيدُ أَنْ أَشُقَّ عَلَيْكَ ۚ سَتَجِدُنِي إِن شَاءَ اللَّهُ مِنَ الصَّالِحِينَ (سورة القصص: 27)

Musa spent years in Shu'aib's household before Allah called him to Prophethood at the burning bush on his journey back toward Egypt. The years of quiet service in Midian, described in Surah Al-Qasas, came directly before the moment his mission as a Messenger began, tying his family life to Shu'aib directly into the larger story of his calling.