Adhan is a call for Muslims to pray five times a day and night. Every time the prayer time is entered, it is recommended to say the adhan so that everyone knows that the prayer time has entered.
Now, after we hear the adhan and answer the adhan as said by the muazzin, we are sunnat or recommended to read the dua after the adhan. The prayer after the adhan that we wrote is a dua that is read after reading sholawat and greetings to the Prophet SAW, then continued by reading the dua after Adhan.
اللَّهُمَّ رَبَّ هَذِهِ الدَّعْوَةِ التَّامَّةِ وَالصَّلاَةِ القَائِمَةِ آتِ سَيِّدَنَا مُحَمَّداً الوَسِيْلَةَ وَالفَضِيْلَةَ، وَابْعَثْهُ مَقَاماً مَحْمُودًا الَّذِي وَعَدْتَهُ إِنَّكَ لَا تُخْلِفُ المِيْعَادَ
رَبِّ اغْفِرْ لِيْ وَلِوَالِدَيَّ وَارْحَمْهُمَا كَمَا رَبَّيَانِيْ صَغِيْرَا
Translitaeration: Allāhumma rabba hāadzihid dakwatit tāmmah, was shalātil qā’imah, āti sayyidanā muhammadanil wasīlata wal fadhīlah, wab‘atshu maqāmam mahmūdanil ladzī wa‘attah, innaka lā tukhliful mī’ād.
Rabbighfir lī, wa li wālidayya, warham humā kamā rabbayānī shaghīrā.
Translation: It means, “O Allah, Lord of the perfect call and standing prayer, give wasilah (place in heaven) and virtue to the Prophet Muhammad. Raise him to a commendable position (right of intercession) that you promised. Indeed, you will not violate your promise.
My Lord, forgive my sins and my parents (sins). Love them both as they loved me when I was little.”
This prayer was narrated by Jabir (one of the companions of the Prophet SAW) in Sahih Bukhari
وعن جابر بن عبد الله رضي الله عنهما أن رسول الله صلى الله عليه وسلم قال من قال حين يسمع النداء اللَّهُمَّ رَبَّ هَذِهِ الدَّعْوَةِ التَّامَّةِ وَالصَّلاَةِ القَائِمَةِ آتِ مُحَمَّداً الوَسِيْلَةَ وَالفَضِيْلَةَ، وَابْعَثْهُ مَقَاماً مَحْمُودًا الَّذِي وَعَدْتَهُ، حلت له شفاعتي يوم القيامة رواه البخاري في صحيحه
“From Jabir bin Abdullah ra, the Messenger of Allah said, ‘Whoever prays when he hears the call to prayer ‘Allāhumma rabba hādzihid dakwatit tāmmah, was shalātil qā’imah, āti muhammadanil wasīlata wal fadhīlah, wab’atshu maqāmam, āti muhammadanil wasīlata wal fadhīlah, wab’atshu maqāmam, āti muhammadanil’ then my intercession is lawful for him on the Last Day.’ (Narrated by Bukhari),” (An-Nawawi, Al-Adzkar, [Cairo, Darul Hadith: 2003 M/1424 H], page 44).
So, whoever reads the dua after adhan, then he will get the intercession or help of the Prophet Muhammad on the Day of Resurrection (yaumul qiayamah). This is a virtue of reciting the prayer after the adhan. So, only by reading the prayer continuously every time you hear the adhan, then you will get the blessing of Rasulullah SAW.