We finish our prayers by saying "al-Salamu Alikum Wa Rahmatullah". Can you tell me upon whom we send the peace and blessings?

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 is His slave and Messenger.

'Ali narrated that the Prophet said: "The key to the prayer is cleanliness (being in the state of purity -i.e. ablution).  The (first) Takbeer of the prayer puts one into inviolable state and the Tasleem releases one from it." [Ahmad, Abu Daawood, An-Nasaa'i, At-Tirmithi and Ibn Maajah]

When a person is in a state of ritual impurity (i.e. not in a state of ablution) he was prohibited from entering the prayer, and by removing this state of impurity, he enters the atmosphere of worship, and by pronouncing Takbeer he actually begins the prayer and then all that was lawful for him outside the prayer becomes forbidden, such as talking, eating, drinking, and by Tasleem the praying person returns to the normal state and all that was forbidden due to the prayer becomes lawful for him.

Therefore, when a praying person performs Tasleem, he should  intend to finish the prayer and to greet the Angels . 

Imaam Al-Hattaab wrote in his book Mawahib Al-Jaleel: "When we make Tasleem we intend to get out of the prayer and to greet the Angels and those who are praying beside us."

Finally, it should be noted that the wordings that are said in acts of worship are acts of worship that one is bound to abide by even if one does not know the wisdom or the purpose behind it."

Allaah Knows best.