The Prophet –may Allah’s peace and blessings be upon him– said: “When the imām says Āmīn, then say Āmīn; for whoever’s Āmīn coincides with the Āmīn of the angels, his previous sins will be forgiven.” Ibn Shihāb said: “And the Messenger of Allah –may Allah’s peace and blessings be upon him– used to say Āmīn.”

Narrated by al-Bukhārī (no. 780, his wording) and Muslim (no. 410), from the narration of Abū Hurayrah –may Allah be pleased with him–.
In another wording by al-Bukhārī (no. 782) and Muslim (no. 410): “When the imām says: {Not of those who have evoked Your anger or of those who are astray}, then say Āmīn...”
In another wording by al-Bukhārī (no. 6402): “When the reciter says Āmīn, then say Āmīn...”
And in another wording by al-Bukhārī (no. 781) and Muslim (no. 410): “When one of you says Āmīn,” and Muslim added: “in the prayer.”

Brief Explanation of the Hadith

The Prophet –may Allah’s peace and blessings be upon him– guided (his ummah) in many aḥādīth to deeds by which Allah multiplies the rewards and grants abundant bounty for little effort.
Among these is what the Prophet –may Allah’s peace and blessings be upon him– informed us of here: that it is prescribed for the follower in prayer to join his imām in saying Āmīn, In such a way that his Āmīn is said concurrently with the Āmīn of his imām, hoping that it will also coincide with the Āmīn of the angels, so that his past sins will be forgiven.
And what is meant by “correspondence” here is correspondence in time — such that the congregant’s saying of Āmīn coincides with the angels’ in both beginning and ending — and it may also include the state of the heart, such as presence, humility, and sincerity in turning to Allah, not merely the matching of words.
And perhaps the wisdom behind this is that such correspondence serves as a sign of attentiveness and humility, for the angels are never heedless; so whoever coincides with them in saying Āmīn, it indicates the presence of his heart and his sincerity. The term “angels” here includes both the angels of the heavens and those on earth, such as the guardian angels and others.
The apparent meaning of the ḥadīth indicates the forgiveness of all sins, both minor and major. However, the majority of scholars have interpreted it as referring to the forgiveness of minor sins, whereas major sins are not forgiven except through repentance that fulfills all its conditions. Likewise, the rights of other people are not included in this promise except through repentance and absolving oneself from those who have rights over him.
The ḥadīth indicates the recommendation of saying “Āmīn” aloud for the imām, the follower, and the individual praying alone in audible prayers.
It also shows the virtue of saying “Āmīn” and that it is one of the causes of forgiveness when it comes from a sincere and devoted heart.