Allah says to His Prophet Muhammad ﷺ:

قُلْ

(Say) O Muhammad to these disbelievers concerning what you have brought to them of this Glorious Qur'an:

ءَامِنُواْ بِهِ أَوْ لاَ تُؤْمِنُواْ

("Believe in it (the Qur'an) or do not believe (in it).) meaning, it is all the same whether you believe in it or not, for it is true in and of itself. It was revealed by Allah, Who mentioned it previously in the Books that He revealed to other Messengers. Hence He says:

إِنَّ الَّذِينَ أُوتُواْ الْعِلْمَ مِن قَبْلِهِ

(Verily, those who were given knowledge before it,) meaning righteous people among the People of the Book, who adhered to their Books and appreciated them without distorting them.

إِذَا يُتْلَى عَلَيْهِمْ

(when it is recited to them,) means, when this Qur'an is recited to them,

يَخِرُّونَ لِلاٌّذْقَانِ سُجَّدًا

(fall down on their chins (faces) in humble prostration. ) means, to Allah, in gratitude for the blessing He has bestowed on them by considering them fit to live until they met this Messenger to whom this Book was revealed. Hence they say:

سُبْحَانَ رَبِّنَآ

(Glory be to our Lord!), meaning, they extol and glorify their Lord for His perfect power and for not delaying the fulfillment of the promise which He made through His earlier Prophets, that He would send Muhammad ﷺ. Hence they said:

سُبْحَانَ رَبِّنَآ إِن كَانَ وَعْدُ رَبِّنَا لَمَفْعُولاً

(Glory be to our Lord! Truly, the promise of our Lord must be fulfilled.)

وَيَخِرُّونَ لِلاٌّذْقَانِ يَبْكُونَ

(And they fall down on their chins (faces) weeping) means, in submission to Allah, may He be glorified, and in expression of their belief and faith in His Book and His Messenger .

وَيَزِيدُهُمْ خُشُوعًا

(and it increases their humility.) means, it increases them in faith and submission. As Allah says:

وَالَّذِينَ اهْتَدَوْاْ زَادَهُمْ هُدًى وَءَاتَـهُمْ تَقُوَاهُمْ

(While as for those who accept guidance, He increases their guidance and bestows on them their Taqwa. ) (47:17).

وَيَخِرُّونَ

(And they fall down) is a description rather than an action (i.e., this is a further description of their humility as referred to in Ayah 107; it does not imply that they prostrate twice).