From Hashiyatul Jamal:
Iqaamatuha (i.e. iqaamatu as-salah): Performing the prayer with composure, protecting it from any sort of deficiency in the fard, sunnah and adab of the prayer.
Others said it refers to being punctual in prayer.
Some say it just means to perform the prayer. Qiyam is part of the prayer. Sometimes the biggest part of a thing is used to refer to the whole thing.
The first meaning is the clearer one, and most popular.
﴿أُوْلَٰـئِكَ عَلَى هُدًى مِّن رَّبِّهِمْ وَأُوْلَٰـئِكَ هُمُ الْمُفْلِحُونَ ﴾
“Ulaa’ika ‘ala hudan” – Ismul ishara has been used as opposed to a pronoun (e.g. “hum ‘ala hudan”) because Ismul Ishara is used for something one can see. These people are so distinguished and clearly known for their attributes that they are referred to in a manner that alludes to them being clearly visible (i.e. being from the “umoorul mushahada”). Ismul Ishara also alludes to “distance”, which in this case would refer to the high rank of these people, and the distance of their level in terms of virtue.
“Hudan” being indefinite has some vagueness in meaning which indicates complete magnification of their guidance, whose reality cannot be reached/grasped and a limit cannot be set on it. That’s why it was left unqualified/unrestricted, without any modifications or limits.
‘Alaa – The preposition ‘alaa (kalimatul isti’laa) has been used to liken their state, with regards to their engagement (mulaabasah) with guidance, to the one who mounts on something and controls it to the point they are able to steer it in whatever direction they like.
Repeating the أُوْلَٰـئِكَ twice, rather than making هُمُ الْمُفْلِحُونَ the 2nd khabr, has a number of benefits:
1) It indicates the increased importance of those who the ismul ishara are referring to, i.e. they are important people worthy of being mentioned more than once.
2) They are on guidance, and they are successful because of the attributes mentioned earlier, e.g. believing in the ghayb, establishing the prayer etc. Mentioning أُوْلَٰـئِكَ twice refocuses attention on those attributes twice as well. The ‘atf coming between the 2 sentences supports this understanding, as it indicates that the two things are different (huda and iflah). Rather iflah is a result of huda. This is in contrast to the below verse where there is no ‘atf in between indicating that both the sentences are referring to the same thing, the latter reinforcing the former:
أُوْلَـٰٓٮِٕكَ كَٱلۡأَنۡعَـٰمِ بَلۡ هُمۡ أَضَلُّۚ أُوْلَـٰٓٮِٕكَ هُمُ ٱلۡغَـٰفِلُونَ
These are as the cattle – nay, but they are worse! These are the neglectful. [7:179]