Salve (sahl-vai), is  a strange Italian word indeed.It is a Latin word — no, it “does not come from” Latin, it actually is Latin! — whose use is attested in Italian in  all epochs. The linguists among you  may like to know it’s the imperative of the verb salvēre, which means being healthy. So,  when we use it we, quite literally, wish our interlocutor to be healthy: salute a te! 

The Romans would use it with vale, which means farewell, in the expression vale atque salve,  “farewell and be healthy,” but our  fellow Italians from the Renaissance used  it as we do today. Salve it’s a strange  word, we were saying, because for quite some time people stopped using it: it felt obsolete and it only lived within the dusty pages of 19th century novels. You’d still hear it here and there, but how awkward it was!