I want to know what the Tahleel and Taqdees which the Prophet, sallallaahu ‘alayhi wa sallam, told us to be steadfast on are, as seen in the following reference?
The Prophet, sallallahu ‘alayhi wa sallam, said, “Hold fast to Tasbeeh, Tahleel, and Taqdees, and close the fingertips, for indeed they shall be questioned, and they will be made to speak. And do not become heedless so that you forget about the Mercy (of Allaah).” [At-Tirmithi; Al-Albaani graded it good in his book Saheeh Al-Jaami‘]

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

Tasbeeh means saying 'Subhaan Allah' (Glory be to Allah), Tahleel means saying 'La ilaaha illa Allah' (There is no god worthy of worship but Allah), Taqdees means saying 'Subhaan Al-Malik Al-Quddoos' (Glory be to The Sovereign, The Most Holy) or 'Subboohun Quddoosun, Rabbu-l-Malaa'ikati war-Rooh' (The Most Glorious, The Most Holy; The Lord of the angels and of Jibreel).

The hadeeth in reference was narrated on the authority of Humaydhah bint Yaasir from her grandmother Yaseerah, who was one of the Muhaajiroon (Emigrants). She reported that the Messenger of Allah, sallallahu ‘alayhi wa sallam, said, “Hold fast to Tasbeeh, Tahleel, and Taqdees, and count them on the fingertips; indeed, they shall be questioned, and they will be made to speak.” [At-Tirmithi, Abu Dawood, Al-Haakim, At-Tabaraani, and Ibn Hibbaan]

Allah knows best.