This is an expression Muslims say whenever they meet one another. It is a statement of greeting with peace. The meaning of it is: "Peace be upon you."
Muslims try to establish peace on earth even through the friendly relation of greeting and meeting one another.
The other forms are: "Assalamu 'Alalikum Wa Rahmatullah," which means:"May the peace and the Mercy of Allah be upon you," and "Assalamu Alalikum Wa Rahmatullahi Wa Barakatuh," which means :"May the peace, the mercy, and the blessings of Allah be upon you."
