Hadith: When the Muezzin (the caller to prayer) says, 'Allahu akbar, Allahu akbar

عن عمر بن الخطاب رضي الله عنه قال: قال رسول الله صلى الله عليه وسلم:
«إِذَا قَالَ الْمُؤَذِّنُ: اللهُ أَكْبَرُ اللهُ أَكْبَرُ، فَقَالَ أَحَدُكُمُ: اللهُ أَكْبَرُ اللهُ أَكْبَرُ، ثُمَّ قَالَ: أَشْهَدُ أَنْ لَا إِلَهَ إِلَّا اللهُ، قَالَ: أَشْهَدُ أَنْ لَا إِلَهَ إِلَّا اللهُ، ثُمَّ قَالَ: أَشْهَدُ أَنَّ مُحَمَّدًا رَسُولُ اللهِ، قَالَ: أَشْهَدُ أَنَّ مُحَمَّدًا رَسُولُ اللهِ، ثُمَّ قَالَ: حَيَّ عَلَى الصَّلَاةِ، قَالَ: لَا حَوْلَ وَلَا قُوَّةَ إِلَّا بِاللهِ، ثُمَّ قَالَ: حَيَّ عَلَى الْفَلَاحِ، قَالَ: لَا حَوْلَ وَلَا قُوَّةَ إِلَّا بِاللهِ، ثُمَّ قَالَ: اللهُ أَكْبَرُ اللهُ أَكْبَرُ، قَالَ: اللهُ أَكْبَرُ اللهُ أَكْبَرُ، ثُمَّ قَالَ: لَا إِلَهَ إِلَّا اللهُ، قَالَ: لَا إِلَهَ إِلَّا اللهُ مِنْ قَلْبِهِ دَخَلَ الْجَنَّةَ».
[صحيح] - [رواه مسلم] - [صحيح مسلم: 385]

‘Umar ibn al-Khattāb (may Allah be pleased with him) reported: The Messenger of Allah (may Allah’s peace and blessings be upon him) said:
"When the Muezzin (the caller to prayer) says, 'Allahu akbar, Allahu akbar' (Allah is the Greatest), and one of you says 'Allahu akbar, Allahu akbar', and then he says, 'Ash'hadu an lā ilāh illa Allah' (I bear witness that there is no god but Allah), and he says, 'Ash'hadu an lā ilāh illa Allah', and then he says, 'Ash'hadu anna Muhammadan rasūl Allah' (I bear witness that Muhammad is the Messenger of Allah), and he says, 'Ash'hadu anna Muhammadan rasūl Allah', and then he says, 'Hayy ‘ala as-salāh' (Come to prayer), and he says, 'Lā hawla wala quwwata illa billāh' (There is no power or strength except through Allah), and then he says, 'Hayy ‘ala al-falāh' (Come to success), and he says, 'Lā hawla wala quwwata illa billāh', and then he says, 'Allahu akbar, Allahu akbar', and he says, 'Allahu akbar, Allahu akbar', and then he says, 'lā ilāh illa Allah', and he says 'lā ilāh illa Allah' from his heart, he will enter Paradise."
[Authentic hadith] - [Narrated by Muslim] - [Sahih Muslim - 385]

Explanation

The Adhan is the call to announce that it is time for one of the obligatory prayers. The words of the Adhān comprise of the creed of faith.
In this Hadīth, the Prophet (may Allah's peace and blessings be upon him) demonstrated what is prescribed upon hearing the Adhān, namely, the hearer of Adhān should say as the Muezzin says. When the Muezzin says, "Allahu akbar", he should say: "Allahu akbar", and likewise with all phrases except when the Muezzin says, "Hayy' ala as-salāh" and "Hayy 'ala al-falāh", upon which the hearer should say: "Lā hawla wala quwwata illa billāh".
The Prophet (may Allah's peace and blessings be upon him) pointed out that whoever repeats after the Muezzin sincerely from his heart will enter Paradise.
The meanings of the phrases of the Adhān: "Allahu akbar": He, Exalted be He, is the most Majestic, the most Sublime, and greater than everything.
"Ash'hadu an lā ilāh illa Allah": No one is truly worthy of worship except Allah.
"Ash'hadu anna Muhammadan rasūl Allah": I acknowledge and testify with my tongue and heart that Muhammad is the Messenger of Allah; Allah Almighty sent him, and it is obligatory to obey him.
"Hayy ‘ala as-salāh": Come to prayer. The listener says "Lā hawla wala quwwata illa billāh" means: There is no way to avoid the things that prevent one from worship, no strength to perform it, and no ability to do anything except with the help of Allah Almighty.
"Hayy ‘ala al-falāh": Come to the cause of success, namely the attainment of Paradise and salvation from Hellfire.