In The Name of Allaah, The Most Merciful, The Bestower of Mercy.

When he says, “الْحَمْدُ لِلَّهِ رَبِّ الْعَالَمِينَ – All the praises and thanks be to Allaah Lord of the entire existence”, he pauses a little to wait for the response of his Lord with the statement “My servant has praised Me”. When he says, “الرَّحْمَنِ الرَّحِيمِ – The Most Merciful, The Bestower of (special) to the believers”, he waits for the response “My servant has exalted Me”. When he says, “مَالِكِ يَوْمِ الدِّينِ – The Only Owner (and the Only Ruling Judge) of the Day of Recompense (i.e. the Day of Resurrection)”, he waits for the response, “My servant has glorified Me”.

What a pleasure for his heart, pleasure of his eyes and happiness of his soul due to the statement of his Lord, “My servant” three times. By Allaah, had there not been the smudge of of desires on the hearts and the murkiness of the souls, they would have sparkle with joy and happiness due to the statement of their Lord, their Originator and object of worship (when He says), “My servant has praised Me”, “My servant has exalted Me” and “My servant has glorified Me”. Then his heart would have had room to draw close attention to these three Names, namely “Allaah”, “Ar-Rabb” and “Ar-Rahmaan”, which are the basis of all the beautiful (and perfect Names). (1)

The complete hadeeth mentioned above is as follows:

Abu Hurairah [may Allaah be pleased with him] reported that the Prophet [peace and blessings of Allaah be upon him] said, “Allah [Almighty] said, “I have divided prayer between Myself and My servant into two halves, and My servant shall have what he has asked for. When the servant says, ‘All praises and thanks be to Allaah, Lord of the entire existence’, Allah says, ‘My servant has praised Me. When he says, ‘The Most Merciful, The Bestower of (special) Mercy to the believers’, Allah says, ‘ My servant has exalted Me’. When he says, ‘The Only Owner (and the Only Ruling Judge) of the Day of Recompense (i.e. the Day of Resurrection)’, Allah says, ‘My servant has glorified’. When he says, ‘You alone we worship, You alone we ask for help’, Allah says, ‘This is between Me and My servant, and My servant will have what he has asked for’. When he says, ‘Guide us to the straight path, the path of those whom you have favored, neither the path of who earned Your anger nor those who went astray”, Allah says, ‘This is for My servant, and My servant will have what he has asked for'”. (2)

Regarding the statement: “I have divided prayer between Myself and My servant into two halves” – Meaning, three and half verses in Surah Al-Faatihah are for the Lord and they are the first part of the Surah. And three and half verses are for the servant and they are the last verses. The first part is about praising Allaah and the last part are supplications for the servant”. (3)

[Ref 1: Kitaab As-Salaah. Page 345-346. Slightly paraphrased]
[Ref 2: Ṣaḥeeh Muslim 395]
[Ref 3: Sharh Ad-Duroos Al-Muhimmah. page 16-17. By Shaikh Abdur Razzaaq Al-Badr]