Salam
There are two instances of this, the context of each slightly changes their meaning.
The first is in Surah Nahl. Some verses to give context in the Surah:
وَعَلَى اللَّهِ قَصْدُ السَّبِيلِ وَمِنْهَا جَائِرٌ ۚ وَلَوْ شَاءَ لَهَدَاكُمْ أَجْمَعِينَ | With Allah rests guidance of the path, and from it are deviations and had He wished He would have guided you all. | An-Nahl : 9
وَيَوْمَ نَبْعَثُ مِنْ كُلِّ أُمَّةٍ شَهِيدًا ثُمَّ لَا يُؤْذَنُ لِلَّذِينَ كَفَرُوا وَلَا هُمْ يُسْتَعْتَبُونَ | The day We shall raise a witness from every nation, the faithless will not be permitted [to speak], nor will they be asked to propitiate [Allah]. | An-Nahl : 84
وَيَوْمَ نَبْعَثُ فِي كُلِّ أُمَّةٍ شَهِيدًا عَلَيْهِمْ مِنْ أَنْفُسِهِمْ ۖ وَجِئْنَا بِكَ شَهِيدًا عَلَىٰ هَٰؤُلَاءِ ۚ وَنَزَّلْنَا عَلَيْكَ الْكِتَابَ تِبْيَانًا لِكُلِّ شَيْءٍ وَهُدًى وَرَحْمَةً وَبُشْرَىٰ لِلْمُسْلِمِينَ | The day We raise in every nation a witness against them from among themselves, We shall bring you as a witness against these. We have sent down the Book to you as a clarification of all things and as guidance, mercy and good news for the Muslims. | An-Nahl : 89
وَلَقَدْ بَعَثْنَا فِي كُلِّ أُمَّةٍ رَسُولًا أَنِ اعْبُدُوا اللَّهَ وَاجْتَنِبُوا الطَّاغُوتَ ۖ فَمِنْهُمْ مَنْ هَدَى اللَّهُ وَمِنْهُمْ مَنْ حَقَّتْ عَلَيْهِ الضَّلَالَةُ ۚ فَسِيرُوا فِي الْأَرْضِ فَانْظُرُوا كَيْفَ كَانَ عَاقِبَةُ الْمُكَذِّبِينَ | Certainly We raised an apostle in every nation [to preach:] ‘Worship Allah, and shun fake deities.’ Among them were some whom Allah guided, and among them were some who deserved to be in error. So travel over the land and observe how was the fate of the deniers. | An-Nahl : 36
Now the mini-context:
الَّذِينَ صَبَرُوا وَعَلَىٰ رَبِّهِمْ يَتَوَكَّلُونَ | —those who are patient and who rely on their Lord. | An-Nahl : 42
وَمَا أَرْسَلْنَا مِنْ قَبْلِكَ إِلَّا رِجَالًا نُوحِي إِلَيْهِمْ ۚ فَاسْأَلُوا أَهْلَ الذِّكْرِ إِنْ كُنْتُمْ لَا تَعْلَمُونَ | And We did not send before you except as men to whom We revealed to therefore ask the family of the Reminder if you do not know. | An-Nahl : 43
بِالْبَيِّنَاتِ وَالزُّبُرِ ۗ وَأَنْزَلْنَا إِلَيْكَ الذِّكْرَ لِتُبَيِّنَ لِلنَّاسِ مَا نُزِّلَ إِلَيْهِمْ وَلَعَلَّهُمْ يَتَفَكَّرُونَ | [We sent them] with manifest proofs and scriptures. We have sent down the reminder to you so that you may clarify for the people that which has been sent down to them, so that they may reflect. | An-Nahl : 44
Mohammad's (s) role to clarify Quran is talked about here in flow, and his family succeed him and take this role. The verse before talks about relying on God and so the "and..." connects asking the family of reminder to the fact it's relying on God.
The other place is in Surah Anbiya. In this Surah, the context is not simply to ask clarification of Quran, but to ask them for miracles. That's seen here:
بَلْ قَالُوا أَضْغَاثُ أَحْلَامٍ بَلِ افْتَرَاهُ بَلْ هُوَ شَاعِرٌ فَلْيَأْتِنَا بِآيَةٍ كَمَا أُرْسِلَ الْأَوَّلُونَ | But they said, ‘[They are] muddled dreams!’ ‘Indeed, he has fabricated it!’ ‘Indeed, he is a poet!’ ‘Let him bring us a sign, like those sent to the former generations.’ | Al-Anbiyaa : 5
مَا آمَنَتْ قَبْلَهُمْ مِنْ قَرْيَةٍ أَهْلَكْنَاهَا ۖ أَفَهُمْ يُؤْمِنُونَ | No town that We destroyed before them believed. Will these then have faith [if they are sent signs]? | Al-Anbiyaa : 6
وَمَا أَرْسَلْنَا قَبْلَكَ إِلَّا رِجَالًا نُوحِي إِلَيْهِمْ ۖ فَاسْأَلُوا أَهْلَ الذِّكْرِ إِنْ كُنْتُمْ لَا تَعْلَمُونَ | And We did not send before you except as men to whom We revealed to therefore ask the family of the Reminder if you do not know. | Al-Anbiyaa : 7
The context is slightly different, in that, in Surah Anbiya, it's talking about signs in form of miracles like previous Messengers were sent with. It warns they most likely won't believe just as past nations who were destroyed did not, but then goes on to say, in the past it was all men who God revealed to as well, therefore go ahead and ask the family of the reminder. The context here is miracles, while in Surah Nahl, the context is about guidance and clarifying what is revealed.
Surah Anbiya emphasizes on the reminder a lot, the new reminder, to be Quran.
Aside from that, we see it also emphasizes on a family of the reminder of the past:
وَوَهَبْنَا لَهُ إِسْحَاقَ وَيَعْقُوبَ نَافِلَةً ۖ وَكُلًّا جَعَلْنَا صَالِحِينَ | And We gave him Isaac, and Jacob as well for a grandson, and each of them We made righteous. | Al-Anbiyaa : 72
وَجَعَلْنَاهُمْ أَئِمَّةً يَهْدُونَ بِأَمْرِنَا وَأَوْحَيْنَا إِلَيْهِمْ فِعْلَ الْخَيْرَاتِ وَإِقَامَ الصَّلَاةِ وَإِيتَاءَ الزَّكَاةِ ۖ وَكَانُوا لَنَا عَابِدِينَ | We made them Imams, guiding by Our command, and We revealed to them [concerning] the performance of good deeds, the maintenance of prayers, and the giving of zakat, and they used to worship Us. | Al-Anbiyaa : 73
And the reminder is both Quran and Mohammad (s). To show this, we read else where:
أَعَدَّ اللَّهُ لَهُمْ عَذَابًا شَدِيدًا ۖ فَاتَّقُوا اللَّهَ يَا أُولِي الْأَلْبَابِ الَّذِينَ آمَنُوا ۚ قَدْ أَنْزَلَ اللَّهُ إِلَيْكُمْ ذِكْرًا | Allah has prepared for them a severe punishment. So be wary of Allah, O you who possess intellect and have faith! Allah has already sent down to you a reminder, | At-Talaaq : 10
رَسُولًا يَتْلُو عَلَيْكُمْ آيَاتِ اللَّهِ مُبَيِّنَاتٍ لِيُخْرِجَ الَّذِينَ آمَنُوا وَعَمِلُوا الصَّالِحَاتِ مِنَ الظُّلُمَاتِ إِلَى النُّورِ ۚ وَمَنْ يُؤْمِنْ بِاللَّهِ وَيَعْمَلْ صَالِحًا يُدْخِلْهُ جَنَّاتٍ تَجْرِي مِنْ تَحْتِهَا الْأَنْهَارُ خَالِدِينَ فِيهَا أَبَدًا ۖ قَدْ أَحْسَنَ اللَّهُ لَهُ رِزْقًا | an apostle reciting to you the manifest signs of Allah that He may bring out those who have faith and do righteous deeds from darkness into light. And whoever has faith in Allah and does righteous deeds, He shall admit him into gardens with streams running in them, to remain in them forever. Allah has certainly granted him an excellent provision. | At-Talaaq : 11
His family is also the same reminder and are the living Quran as well whence the fullest appreciation of it's glory and beauty is found, and hence "the family of the reminder".
