Verse 86 of Surah Nisaa’ mentions تَحِيَّة which is in the context of a greeting. It is a prayer that Allah ta’ala keeps the person alive in peace.
It is a deep and beautiful concept of conveying a prayer (Du’a) of peace till eternity unlike the various greetings of other cultures. The person making the Salaam is conveying to the other person that there is going to be Aman/Salaamati from him/her i.e. he will be protected.
As-Salaam is the Sifat of Allah ta’ala
Since the word As-Salaam is also one of the attributes of Allah ta’ala, certain commentators have mentioned that when one greets, it means,
May Allah, who is the giver of peace, take you in His safety and custody, keeping you in peace forever.
There is so much beauty in the Salaam however we take it for granted. Let us be mindful of these beautiful points when greeting others with Salaam as it is giving each other a very powerful Du’a