Some people believe that the Hebrew word "Shalom" (שלום) means "peace". However this is not exactly the case. Some people also believe as a result that Islam means "religion of peace", but this is also certainly not the case. This is due to lack of understanding of the Semitic root S.L.M. or Sh.L.M.
In many Semitic languages there was a general duality between the "S" and "Sh" sounds. In the Hebrew alphabet, the same letter - ש - is used for both sounds. So S.L.M can also be Sh.L.M in some cases. In Semitic languages there's a three-letter or four-letter root for verbs and other words, and there are several ways to transform them.
Now the verb S.L.M. is a Semitic root that has a general meaning of wholeness, fullness or completeness. In Hebrew, "Shalam" used to mean ended, but it is no longer really used. "Nishlam" means "ended" as well, and its use is more common, but a bit archaic. "Shilem" is paid for, "Shulam" is was paid for. "Hishtalem" (derived from "Hitshalem") is was worthwhile, or more recently got an extra education. "Hishlim" is completed, and "Huslam" is "was completed".
Now "Shalom" is essentially "well-being" - a state where nothing bad happens. In the political field, it means "peace", but in fact the early word for such peace in Hebrew was "Sheqet" which means "quiet". Judges 3 - "Wa'tishqot ha'aretz Shmonim Shanah" - "and the land was quiet for 80 years".
Shalom is not necessarily about peace between countries. For example one can say "The United States government will do everything to ensure the 'Shalom' of the passengers of the kidnapped plane". And then there was "Milhhemeth Shlom-Hagalil" ("מלחמת שלום-הגליל") which was the "war for the Shalom [or well-being] of the Galilee".
Now about Islam - Islam is the noun form of the Arabic verb "Aslama", which means converted to Islam. Aslama, being S.L.M. was meant to mean a "Complete devotion to one's faith." Similarly "Muslim" (pronounced "Mooss-leem")is someone who is an Islam practictioner. Peace or even well-being have nothing to do with it.