"Salem alekem," which is more commonly spelled "salaam alaikum," means "peace to you" in Arabic. It is a common greeting used by Muslims throughout the world, and is therefore somewhat akin to "hello."
The traditional response to "salaam alaikum" or "assalaam alaikum" is "wa alaikum assalaam," which means "and unto you peace." The phrase and its response have many spellings in English. This diversity of spellings comes from the many different English-Arabic transliteration systems in use. The Arabic phrase "salaam alaikum" is very similar to the Hebrew phrase "shalom aleichem" and the more informal "shalom," which Hebrew speakers often use to greet each other.