O Allah! You are Salam

بسم الله الرحمن الرحيم

The Prophet of Allāh sallallāhu ‘alayhi wa sallam would say at the end of every prayer, اللَّهُمَّ أَنْتَ السَّلَامُ، وَمِنْكَ السَّلَامُ، تَبَارَكْتَ يَا ذَا الْجَلَالِ وَالْإِكْرَامِ (O Allāh! You are As-Salām and from you is as-salām. Most Blessed are You, O Owner of Majesty and Honour)” [Ibn Mājah].

O Allāh! You are As-Salām
As-Salām is one of Allāh’s Names. The word salām linguistically comes from a root which means freedom or safety from any number of things. Accordingly, As-Salām as a Name of Allāh denotes One who is Serene in His Existence, Beautiful in His Conduct and Flawless in every way because He is free of every deficiency, high above any susceptibility to harm, innocent of any fault or indecorum. 
This perfection (or salāmah) is witnessed in all of Allāh’s Attributes. For example, He is Al-‘Alīm (Knowing) without the imperfection of ignorance and forgetfulness. He is Al-Hayy (Living) without the imperfection of death and ill health.
And from You is as-salām
This is a type of implicit supplication (du‘ā). (This supplication is a request for ‘safety’ and ‘perfection’ which is elaborated on further below).
A supplication or request is worded either explicitly or implicitly. 
An example of an implicit supplication is the du‘ā of Ayyūb ‘alayhis-salām, “And (remember) Ayyūb when he called out to his Lord, ‘Indeed, harm has touched me and You are the Most Merciful of those who show mercy.’” [21:83] 
There is no explicit request for relief. He could have explicitly said, “I was a rich, healthy man with a loving family. Now, I have been bereft of my wealth, my health and my family. Relieve me of all this. O Allāh! Return to me to what I had lost.” 
Similarly, Yūnus sought relief in the belly of the whale, saying, “There is no deity but You, Glorified be You! Truly, I have been of the wrongdoers.” [21:87] And Allāh answered, “So, We responded to him and saved him from the distress. And thus do We save the believers.” [21:88]
Most Blessed are You, O Owner of Majesty and Honour
This is a reiteration of Allāh’s perfect condition.
The implicit request
Upon finishing the prayer, the Muslim makes this request after the istighfār (astaghfirullāh x3). Through the istighfār he seeks forgiveness for the heedlessness and shortcomings in the salāh, whilst through “Allāhumma antas-Salām…” he seeks perfection in the next. This is his mindset for the succeeding prayer.
In other words, “O Allāh! You are Beautiful, Serene and Flawless in every way (As-Salām). Make my prayer beautiful, serene and flawless. Only then can it be worthy of being directed towards You because You are Beautifully Perfect and You alone deserve beautiful, perfect worship.”

والحمد لله رب العالمين
وصلى الله وسلم على نبينا محمد

Abu Unays