The first meaning is the common meaning which all of us know, “Peace be upon you.” What a great greeting?
If a person has peace in his health, wealth, finances, business, life, a person has got everything. If a person does not own any money yet he has peace, he has obtained everything.
Secondly, “Assalam” is the name of Allah Ta'ala. When a person greets another it means, “May Allah Ta'ala be with you.”
Imagine what a great Dua this is, you are telling someone that “May Allah be with you.”
This is like a father that was at home throughout the night. When leaving home in the morning it is as though he is telling the family, “I was with you all the time and now you will all be alone, so may Allah be with you!” What a spiritual support has he left behind?
The family replies, Wa’laikum-Us-Salaam making Dua that may Allah be with you...