As-Salãmu ‘Alaykum(in Arabicالسَّلَامُ عَلَيْكُمْ) is a statement of greeting meaning
‘peace be upon you’. The appropriate response is Wa ‘Alaykumus-Salam,
meaning ‘and peace be upon you also’.
It is interesting to find the same the same greeting used in the Bible by Jesus:
Luke 24:36 (King James Version)
36 And as they thus spake, Jesus himself stood in the midst of them, and saith unto them, Peace be unto you.