When the Imām says amen, you too say amen, for whoever says amen at the same time the angels say amen will have his previous sins forgiven
Authentic hadithعن أبي هريرة رضي الله عنه مرفوعاً: «إذا أَمَّنَ الإمام فأمنوا، فإنه من وافق تأمينه تأمين الملائكة: غفر له ما تقدم من ذنبه».
Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "When the Imām says amen, you too say amen, for whoever says amen at the same time the angels say amen will have his previous sins forgiven."
Explanation
The Prophet (may Allah's peace and blessings be upon him) ordered us to say 'amen' when the Imām says it because this is the time when the angels say 'amen', and whoever says it at the same time as the angels his previous sins will be forgiven.
Source · Narrated by Bukhari & Muslim
From the Hadith Encyclopedia (hadeethenc.com).