Abu Hurairah reported the Messenger of Allah ﷺ as saying; Glorifying Allah applies to men and clapping applies only to women.  

قَالَ رَسُولُ اللَّهِ ﷺ التَّسْبِيحُ لِلرِّجَالِ وَالتَّصْفِيقُ لِلنِّسَاءِ  

The Messenger of Allah ﷺ went to Banu ‘Amr b. ‘Awf to effect reconciliation between them . in the meantime the time of prayer came and the Mu’adhdhin came to Abu Bakr and asked : Will you lead the people in prayer? I pronounce the Iqamah. He said ; Yes. So Abiu Bakr led the prayer , and the Messenger of Allah ﷺ came back while the people were praying. He penetrated through the rows and stood in the first row. The people clapped but Abu Bakr did not pay any attention to it during prayer. When the people clapped increasingly, he paid attention. He saw the Messenger of Allah ﷺ. The Messenger of Allah ﷺ made a sign to him (saying); Stay at your place. Abu BAkr raised his hands and praised Allah for the commandment the Messenger of Allah ﷺ had given him (to lead the people in prayer). Abu Bakr then stepped back and stood in the row. The Messenger of Allah ﷺ stepped forward and led the prayer. When he finished the prayer, he said; Abu Bakr, what prevented you staying (at your place) when I already commented you to do so? Abu Bakr said ; it was not befitting for the son of Abu Quhafah (Abu Bakr) to lead the prayer in the presence of the Messenger of Allah ﷺ. The Messenger of Allah ﷺ said; What is the matter that I saw you clapping frequently during prayer? If anything happens to someone during prayer, he should say “Glory be to Allah,” for when he glorifies Allah. He pays attention to him. Clapping applies only to women. Abu Dawud said: This is operative in the obligatory prayer.  

أَنَّ رَسُولَ اللَّهِ ﷺ ذَهَبَ إِلَى بَنِي عَمْرِو بْنِ عَوْفٍ لِيُصْلِحَ بَيْنَهُمْ وَحَانَتِ الصَّلاَةُ فَجَاءَ الْمُؤَذِّنُ إِلَى أَبِي بَكْرٍ ؓ فَقَالَ أَتُصَلِّي بِالنَّاسِ فَأُقِيمَ قَالَ نَعَمْ فَصَلَّى أَبُو بَكْرٍ فَجَاءَ رَسُولُ اللَّهِ ﷺ وَالنَّاسُ فِي الصَّلاَةِ فَتَخَلَّصَ حَتَّى وَقَفَ فِي الصَّفِّ فَصَفَّقَ النَّاسُ وَكَانَ أَبُو بَكْرٍ لاَ يَلْتَفِتُ فِي الصَّلاَةِ فَلَمَّا أَكْثَرَ النَّاسُ التَّصْفِيقَ الْتَفَتَ فَرَأَى رَسُولَ اللَّهِ ﷺ فَأَشَارَ إِلَيْهِ رَسُولُ اللَّهِ ﷺ أَنِ امْكُثْ مَكَانَكَ فَرَفَعَ أَبُو بَكْرٍ يَدَيْهِ فَحَمِدَ اللَّهَ عَلَى مَا أَمَرَهُ بِهِ رَسُولُ اللَّهِ ﷺ مِنْ ذَلِكَ ثُمَّ اسْتَأْخَرَ أَبُو بَكْرٍ حَتَّى اسْتَوَى فِي الصَّفِّ وَتَقَدَّمَ رَسُولُ اللَّهِ ﷺ فَصَلَّى فَلَمَّا انْصَرَفَ قَالَ يَا أَبَا بَكْرٍ مَا مَنَعَكَ أَنْ تَثْبُتَ إِذْ أَمَرْتُكَ قَالَ أَبُو بَكْرٍ مَا كَانَ لاِبْنِ أَبِي قُحَافَةَ أَنْ يُصَلِّيَ بَيْنَ يَدَىْ رَسُولِ اللَّهِ ﷺ فَقَالَ رَسُولُ اللَّهِ ﷺ مَا لِي رَأَيْتُكُمْ أَكْثَرْتُمْ مِنَ التَّصْفِيحِ مَنْ نَابَهُ شَىْءٌ فِي صَلاَتِهِ فَلْيُسَبِّحْ فَإِنَّهُ إِذَا سَبَّحَ الْتُفِتَ إِلَيْهِ وَإِنَّمَا التَّصْفِيحُ لِلنِّسَاءِ  

sahl b. Sa’d said; Fighting took place amongst the tribe of Banu ‘Amr b. ‘Awf. This (the news) reached the prophet (May peace be upon him). He came to them for their reconciliation after the noon prayer . he said to Bilal; If the time of the afternoon prayer comes, and I do not return to you, then ask Abu Bakr to lead the people in prayer. When the time of the afternoon prayer came, Bilal called the Adhan and pronounced the Iqamah and then asked Abu Bakr (to lead the prayer). He stepped forward. The narrator reported this tradition to the same effect. In the end he (the prophet) said; if anything happens to you during prayer, the men should say” Glory be to Allah,” and the women should clap.  

كَانَ قِتَالٌ بَيْنَ بَنِي عَمْرِو بْنِ عَوْفٍ فَبَلَغَ ذَلِكَ النَّبِيَّ ﷺ فَأَتَاهُمْ لِيُصْلِحَ بَيْنَهُمْ بَعْدَ الظُّهْرِ فَقَالَ لِبِلاَلٍ إِنْ حَضَرَتْ صَلاَةُ الْعَصْرِ وَلَمْ آتِكَ فَمُرْ أَبَا بَكْرٍ فَلْيُصَلِّ بِالنَّاسِ فَلَمَّا حَضَرَتِ الْعَصْرُ أَذَّنَ بِلاَلٌ ثُمَّ أَقَامَ ثُمَّ أَمَرَ أَبَا بَكْرٍ فَتَقَدَّمَ قَالَ فِي آخِرِهِ إِذَا نَابَكُمْ شَىْءٌ فِي الصَّلاَةِ فَلْيُسَبِّحِ الرِّجَالُ وَلْيُصَفِّحِ النِّسَاءُ  

Clapping by women means that one should strike her left hand with the two fingers of her right hand.  

قَوْلُهُ التَّصْفِيحُ لِلنِّسَاءِ تَضْرِبُ بِأُصْبُعَيْنِ مِنْ يَمِينِهَا عَلَى كَفِّهَا الْيُسْرَى