The Azan is the arabic term for the call to prayer. When the Azan for Salah is called out it is mustahab (rewarding) to reply to the Azan by repeating the words after the Muazzin. This practice has been encouraged in a number of Ahadith.
Hazrat Abdullah ibn Amr ibn Aas (R) reports that Rasulullah (Sallallahu Alaihi Wasallam) said, “When you hear the Muazzin then repeat what he says …” (Sahih Muslim)
Hazrat Umar (R) narrates that Rasulullah (Sallallahu Alaihi Wasallam), “When the Muazzin says 'Allahu Akbar Allahu Akbar' then the one who says 'Allahu Akbar Allahu Akbar' …(and continuous mentioning the other words of the Azan)…, - when (the Muazzin) says Lailaha Illallah, then the one who says Lailaha Illallah from the heart (with conviction), will enter Jannah.” (Sahih Muslim)
Hazrat Abu Hurairah (R) narrates, “We were with Rasulullah (Sallallahu Alaihi Wasallam) when Hazrat Bilal (R) stood up to call out the Azan. When he completed the Azan, Rasulullah (Sallallahu Alaihi Wasallam) said, 'Whoever says these words with conviction will enter Jannah.'” (Sunan Nasai)
It is understood from these Ahadith that in addition to responding to the Azan by proceeding for Salah, we should also respond to the words of the Azan.
At Hayya alas Salah and Hayya alal Falah, these words should be repeated after the Muazzin and additionally La hawla wala quwwata illa billah should be recited.
When the Azan commences, all activities should be suspended and the Azan should be responded to with complete attention. If a person is engaged in the recitation of the Qur'an it is recommended to stop recitation and reply to the Azan. However, those engaged in learning and teaching of Deen may continue and reply after the Azan is complete.