What is the meaning and interpretation of the complete Tashahhud upon finishing the prayer?

Authentic hadiths concerning the Tashahhud have been reported from the Prophet, peace and blessings be upon him. Among the strongest of these is what was narrated by Al-Bukhari and Muslim from Abdullah ibn Mas'ud, may Allah be pleased with him, with the wording: "All greetings [tahiyyat] are for Allah, and all prayers [salawat] and good things [tayyibat]. Peace be upon you, O Prophet, and the mercy of Allah and His blessings. Peace be upon us and upon the righteous servants of Allah. I bear witness that there is no god but Allah, and I bear witness that Muhammad is His servant and His Messenger."

Meaning of the words: Al-Tahiyyat: Exaltation for Allah, or sovereignty, or safety from afflictions. Al-Salawat: Supplication or the five daily prayers. Al-Tayyibat: Righteous deeds or pure speech. Peace be upon you, O Prophet: May Allah's name be upon you, or may Allah grant you peace. Upon us: The Imam, the congregants, the angels, and others. Righteous servants of Allah: Those who fulfill the rights of Allah and the rights of His servants.

As for the worshiper's saying in the taslim: "Peace be upon you and the mercy of Allah": this is a supplication for the believers for preservation, safety, and mercy from Allah. "Peace [Al-Salam]" here is either one of Allah's names, in which case the meaning is: May Allah's name be upon you, meaning you are under His protection. Or it is a verbal noun meaning safety, i.e., I supplicate for your safety.