What is meant by standing in the obligatory prayer, and by ṭuma’nīnah (tranquility), and by tartīb (sequential order) as pillars of prayer?

A pillar (rukn) is that without which something is not valid, and it is part of its essence.

Firstly: Standing in the obligatory prayer is a duty for the able, such as the five daily prayers, Jumu'ah prayer, and communal obligations (fard al-kifayat). Standing is waived for one who is afraid, one who is naked and cannot find covering, a sick person whose illness cannot be treated while standing, and one who is unable to exit a place with a low ceiling. Sitting is permissible in supererogatory prayers, though with reduced reward.

Secondly: Tranquility (ṭumaʾnīnah) is a pillar in all the pillars of prayer according to the majority of scholars. Its minimum is the stillness of the limbs for the duration of saying "Subhan Allah" (Glory be to Allah).

Thirdly: The order (tartīb) among the pillars means that the pillars must be arranged as they were narrated from the Prophet, peace and blessings be upon him, such as the opening takbir before Al-Fatihah, and Al-Fatihah before bowing, and so on.