Assalamu alaykum wa rahmatu allah wa barakatuh. This is the Islamic greeting in Arabic with which Muslims greet each other and greet the Angels when entering the house, or any building and when entering the Masjid.
Prophet Muhammad, Peace Be Upon Him, said:
Allah, the Exalted and Glorious, created Adam in his own image with his height of sixty cubits, and as He created him He told him to greet that group, which was a party of angels sitting there, and listen to the response that they give him, for it would form his greeting and that of his offspring. He then went away and said: Peace be upon you! They (the angels) said: May there be peace upon you and the Mercy of Allah, and they made an addition of "Mercy of Allah". So he who would get into Paradise would get in the form of Adam, his length being sixty cubits, then the people who followed him continued to diminish in size up to this day. Source: al-islam
Spreading Peace
When ye are greeted with a greeting, greet ye with a better than it or return it. Lo! Allah taketh count of all things. The Women 4:86
No blame is there upon the blind nor any blame upon the lame nor any blame upon the sick nor on yourselves if ye eat from your houses, or the houses of your fathers, or the houses of your mothers, or the houses of your brothers, or the houses of your sisters, or the houses of your fathers' brothers, or the houses of your fathers' sisters, or the houses of your mothers' brothers, or the houses of your mothers' sisters, or (from that) whereof ye hold the keys, or (from the house) of a friend. No sin shall it be for you whether ye eat together or apart. But when ye enter houses, salute one another with a greeting from Allah, blessed and sweet. Thus Allah maketh clear His revelations for you, that haply ye may understand. Al Noor 24:61
If a person does not greet people or reply to their greeting due to arrogance, s/he loses a great reward from God. The person will be viewed differently by the people around him/her. And can lose their friendship or trust.
And sometimes there can be misunderstandings or quarrels between people. They do not talk for 2 days. Be careful not to be enemies for more than three days! Allah's Messenger, Peace Be Upon Him, said:
It is not lawful for a Muslim to desert his fellow Muslim beyond three nights, the one turning one way and the other turning the other way when they meet; the better of the two is the one who is the first to give a greeting. Source: al-islam
Neither nurse mutual hatred, nor jealousy, nor enmity, and be as fellow-brothers and servants of Allah. It is not lawful for a Muslim to desert his brother Muslim beyond three days. Source: al-islam