The meaning of blessings and salaams upon the Prophet (peace and blessings of Allah be upon him)
Question

What is the meaning of blessings and salaams upon the Prophet (peace and blessings of Allah be upon him)?.
Praise be to Allah.“Blessings upon the Prophet (peace and blessings of Allah be upon him)” – according to the majority of scholars, what is meant is mercy from Allah, prayers for forgiveness offered by the angels, and du`a offered by humans. Others – including Abu’l-Aaliyah among the earlier scholars and Ibn al-Qayyim among the later scholars, and Ibn ‘Uthaymeen among the contemporary scholars – are of the view that the meaning of blessings upon the Prophet (peace and blessings of Allah be upon him) is praise for him among the “higher group” (al-mala’ al-‘a’la, i.e., the angels, cf. al-Saffaat 37:8), and the prayers of the angels and the Muslims for blessings upon him (peace and blessings of Allah be upon him) are for him to be praised by Allah among the “higher group” (the angels). Ibn al-Qayyim (may Allah have mercy on him) wrote a book on this topic entitled Jala’ al-Afhaam fi Fadl al-Salaati wa’l-Salaam ‘ala Khayr il-Anaam, in which he discussed at length the meaning of blessings upon the Prophet (peace and blessings of Allah be upon him), the rulings thereon, and its benefits.  
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: 
The phrase “Bless Muhammad (salli ‘ala Muhammad)” – it was said that blessing from Allah means mercy, blessings from the angels means prayer for forgiveness, and blessing from humans means du`a. 
If it is said: “The angels sent blessings upon him,” it means that they prayed for forgiveness for him.  
If it is said, “The khateeb sent blessings upon him,” it means that he prayed for blessing for him. 
If it is said, “Allah sent blessings upon him,” it means that He bestowed mercy upon him. 
This is well known among the scholars, but the correct view is something different, because blessing (salaah) is more specific than mercy. Hence the Muslims are unanimously agreed that it is permissible to pray for mercy for every believer, but they differed as to whether we may pray for blessings (using this specific word of salaah or salli ‘ala…) for anyone other than the Prophets. If the word salaah here is taken to mean mercy, then there is no difference between them, and just as we pray for mercy for a person we may send blessings upon them. 
Moreover, Allah says (interpretation of the meaning): 
“They are those on whom are the Salawaat (i.e. who are blessed and will be forgiven) from their Lord, and (they are those who) receive His Mercy, and it is they who are the guided ones” [Al-Baqarah 2:157]. 
The word rahmah (mercy) is mentioned in conjunction with the word salawaat (blessings), which indicates that they are two different things, so the meaning of the verse is clear. The scholars (may Allah have mercy on them) used the word salaah (blessings) in some places and the word rahmah (mercy) in others, so salaah is the not the same as mercy. The best that cane be said concerning this is what Abu’l-‘Aaliyah (may Allah have mercy on him) said: The salaah (blessing) of Allah upon the Prophet (peace and blessings of Allah be upon him) is His praising him among the “higher group” (the angels). 
So what is meant by Allahumma salli ‘alayhi (O Allah send blessings upon him) is: O Allah, praise him among the higher group, i.e., among the angels who are close to Allah. 
If someone were to say that this is unlikely from a linguistic point of view, because salaah in Arabic means supplication, not praise, the answer to that is that the word salaah is also connected to the word silah (gift), and there can be no doubt that praise for the Messenger of Allah (peace and blessings of Allah be upon him) among the higher group (angels) is one of the greatest gifts, for praise may sometimes be more important to a person than all else. So a good mention is a great gift. 
Based on this, the correct view is that sending blessings (salaah) upon him means praise for him along the higher group (the angels)."(Al-Sharh al-Mumti’, 3/163, 164 )
With regard to the meaning of sending salaams upon him (peace and blessings of Allah be upon him), this means praying for the soundness (salaamah) of his body during his lifetime, and the soundness of his religious commitment (peace and blessings of Allah be upon him), the soundness of his body in the grave, and his safety and well being on the Day of Resurrection. 
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: 
The phrase al-salamu ‘alayka. It was said that the meaning of al-Salaam is one of the names of Allah, because the Prophet (peace and blessings of Allah be upon him) said: “Allah is al-Salaam (the One Free from all defects)” and Allah says in His Book (interpretation of the meaning): “the King, the Holy, the One Free from all defects” [al-Hashr 59:23]. So according to this view, the meaning is: May Allah protect, keep safe and take care of His Messenger (peace and blessings of Allah be upon him). It is as if we are saying: Allah is watching over you, protecting you, helping you, etc.  
And it was said that salaam is a noun that comes from the root sallama (to greet), and means a greeting, as Allah says (interpretation of the meaning): “O you who believe! send your Salaah on (ask Allah to bless) him (Muhammad), and (you should) greet (salute) him with the Islamic way of greeting (salutation, i.e. As‑Salamu ‘Alaykum)” [al-Ahzaab 33:56]. The meaning of greeting the Messenger (peace and blessings of Allah be upon him) is to pray for him and ask that he be kept safe from all harm.  
It may be said: This du`a is something obvious during his lifetime, (peace and blessings of Allah be upon him), but after his death, how can we pray that he be kept safe and sound when he (peace and blessings of Allah be upon him) has died? 
The answer is that prayer for safety and well-being are not limited to the time when someone is alive. There are the terrors of the Day of Resurrection yet to come. Hence the prayer of the Messengers when the people cross al-siraat (a bridge over Hell) will be: “Allahumma, sallim, sallim (O Allah, grant safety, grant safety).” A man does not cease to face danger and harm just because he has died. 
So we pray for the Prophet (peace and blessings of Allah be upon him), that he will be kept safe from the terrors of the standing (on the Day of Resurrection). 
We also say that there may be a more general meaning, i.e., that safety and protection for him also includes protection for his sharee’ah and Sunnah, that they may be kept safe from the hands of those who would tamper with them, as the scholars said concerning the verse (interpretation of the meaning): “refer it to Allah and His Messenger” [Al-Nisa’ 4:59] – they said: Refer to him during his lifetime, and to his Sunnah after his death. 
Is the phrase “al-salamu ‘alayka” a statement or a du`a? i.e., are you saying that the Messenger is protected, or are you praying that Allah will protect him? 
The answer is that it is a du`a, asking that Allah will protect him. So it is a statement that serves as a du`a.
 Is addressing the Messenger (peace and blessings of Allah be upon him) like one person addressing another? 
The answer is no. If that were the case, then the prayer would be invalidated thereby, because no ordinary human speech is acceptable during this prayer. If that were the case, the Sahaabah would have said it out loud so that the Prophet (peace and blessings of Allah be upon him) would hear them, and he would have returned the greeting, as happened when they met him. But, as Shaykh al-Islam [Ibn Taymiyah] said in his book Iqtida’ al-Siraat al-Mustaqeem: Because you think so much about the Messenger (peace and blessings of Allah be upon him) when you send salaams upon him, it is as if he is in front of you and you are addressing him. 
Hence the Sahaabah used to say “Al-salamu ‘alayka” although he could not hear them, and they would say “Al-salamu ‘alayka” when they were in one land and he was in another, and we say “al-salamu ‘alayka” although we are in lands other than his, and in a time other than his.'(Al-Sharh al-Mumti’, 3/149, 150)
And Allah knows best.