All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
The famous narrations of this Hadeeth highlight that the Prophet, sallallaahu ‘alayhi wa sallam, said these words to his Companions . Jaabir ibn Samurah said, "The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, came out once as we were praying and said: “Why do I see you raising your hands like the tails of horses? Be tranquil in prayer.” [Muslim, Ahmad, Abu Daawood, An-Nasaa'i, At-Tirmithi, Ibn Maajah and others]
Other versions of this narration have shed light on the forbidden type of raising hands during prayer. Jaabir ibn Samurah and others said, "When we performed prayer with the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, we used to make Tasleem (i.e. saying As-Salaamu ‘alaykum wa Rahmatullah) while moving our two palms when ending the prayer towards the right and the left. The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, said to us: "Why do you point out with your hands as if they are the tails of headstrong horses. It is enough for any of you that he should place his hand on his thigh and then pronounce the salutation upon his brother to his right side and his left." [Muslim and others]
This narration clarified that the Companions used to move their two palms when ending the prayer towards the right and the left, so the Prophet, sallallaahu ‘alayhi wa sallam, prohibited them from doing that.
As for raising the hands during Takbeerat Al-'Ihraam (i.e. Opening Takbeerah) or before or after the Rukoo‘ (i.e. bowing), it is a reported act of Sunnah as is cited in Saheeh Al-Bukhari and Saheeh Muslim from the Hadeeth of Ibn Umar as he said, "The Messenger of Allaah, sallallaahu ‘alayhi wa sallam, used to raise his hands to the level of his shoulders when beginning the prayer, when saying Allaahu Akbar, when bowing down and when standing up from Rukoo‘, but he did not raise them when raising his head from prostration." [Muslim]
Allaah Knows best.