Narrated Ibn `Abbas:
Regarding His (Allah's) Statement:-- 'Move not your tongue concerning (the Qur'an) to make haste therewith.' (75.16) And whenever Gabriel descended to Allah's Messenger (ﷺ) with the Divine Inspiration, Allah's Messenger (ﷺ) used to move his tongue and lips, and that used to be hard for him, and one could easily recognize that he was being inspired Divinely. So Allah revealed the Verse which occurs in the Surah starting with "I do swear by the Day of Resurrection.' (75.1) i.e. 'Move not your tongue concerning (the Qur'an) to make haste then with. It is for Us to collect it (in your mind) (O Muhammad) an give you the ability to recite it 'by heart.' (75.16-17) which means: It is for us to collect it (in your mind) and give you the ability to recite it by heart. And when We have recited it to you (O Muhammad) through Gabriel then follow you its recital. (75.18) means: 'When We reveal it (the Qur'an) to you, Listen to it.' for then: It is for Us to explain it and make it clear to you' (75.19) i.e. It is up to Us to explain it through your tongue. So, when Gabriel came to him, Allah's Messenger (ﷺ) would listen to him attentively, and as soon as Gabriel left, he would recite the Revelations, as Allah had promised him.
Narrated Musa bin Abi `Aisha:
Sa`id bin Jubair reported from Ibn `Abbas (regarding the explanation of the Verse: 'Do not move your tongue concerning (the Qur'an) to make haste therewith) . He said, "The Prophet (ﷺ) used to undergo great difficulty in receiving the Divine Inspiration and used to move his lips.' Ibn `Abbas said (to Sa`id), "I move them (my lips) as Allah's Messenger (ﷺ) used to move his lips." And Sa`id said (to me), "I move my lips as I saw Ibn `Abbas moving his lips," and then he moved his lips. So Allah revealed:-- '(O Muhammad!) Do not move your tongue concerning (the Qur'an) to make haste therewith. It is for Us to collect it and give you (O Muhammad) the ability to recite it. (i.e., to collect it in your chest and then you recite it).' (75.16-17) But when We have recited it, to you (O Muhammad through Gabriel) then follow you its recital.' (75.18) This means, "You should listen to it and keep quiet and then it is upon Us to make you recite it." The narrator added, "So Allah's Messenger (ﷺ) used to listen whenever Gabriel came to him, and when Gabriel left, the Prophet (ﷺ) would recite the Qur'an as Gabriel had recited it to him."