Arabs before Islam were greeting by: Allah bless you, however, after Islam it became: Assalamu alaykum (Peace be upon you):

 تَحِيَّتُهُمْ يَوْمَ يَلْقَوْنَهُ سَلَامٌ ۚ وَأَعَدَّ لَهُمْ أَجْرًا كَرِيمًا

(Their greeting the Day they meet Him will be, “Peace.” And He has prepared for them a noble reward.) (Al-Ahzab: 44)

This greeting has a great meaning. It is required to spread greeting among people and to implement this word in practice. Peace is security and reassurance, so when you greet others, you give security and reassurance, and you ensure that good reaches others and that evil does not affect them, so you withhold your evil from them and giving them your goodness. Every murderer, every adulterer, every thief, every violator of honor, every criminal and rapist does not actually give peace because he transmits evil to others, so where is he from peace and its spread!!

So the meaning of Islam in general is peace, and the Arabic word of Islam is derived from the Arabic word of peace (Salam).

A man came to the Messenger of Allah and said, “As-Salamu `Alaykum”. The Prophet said: Wa-alaikum As-Salam Wa Rahmatu llahi, then another man came and said, “As-Salamu `Alaykum wa Rahmatullah, O Allah’s Messenger.” The Prophet said:  Wa-alaikum As-Salam wa Rahmatu llahi wa Barakatuh” Then another man came and said, “As-Salamu `Alaykum wa Rahmatullah wa Barakatuh.” The Prophet said: “Wa alayk”, so the man said: O’ messenger of Allah, the two men have greeted you and you replied with better than you greeted me! The Prophet (saws) said: “You have left nothing and Allah is saying: (And when you are greeted with a greeting, greet [in return] with one better than it or [at least] return it), so that I returned the greeting to you.