Jerusalem (Hebrew יְרוּשָׁלַיִם Yerushalayim) was a Canaanite city which King David made the capital of Israel. It has a long history, both literally and figuratively, as a holy city in Judaism, Christianity and Islam (in Arabic it is called أورشليم) القدس) al-Quds or Urshalim al-Quds). It was built on a mountain called Zion, hence "Zion" is often used as a synonym of "Jerusalem". Jerusalem is also often equated to the Salem of which Melchizedek was high priest according to Genesis 14:18-20. As "the city of God" (the location of Solomon's Temple), the name Jerusalem has also been used of the "New Jerusalem", the eschatological city of God. In addition to Salem and Zion, other names of Jerusalem include Solyma (from the Greek Ιεροσόλυμα "Holy Salem"), Moriah and Ariel — among many others.
Although Jerusalem often refers to the New Jerusalem and to Zion, it is believed that they are not always the same thing - that the New Jerusalem and Zion are synonymous, but that the old Jerusalem is a different place (the old one being the city that existed in Bible times). Zion in the Bible may also have referred to the old Jerusalem, at times (seeing as Zion may refer to many things - even to the collective followers of God who are members of his church). Zion, or the New Jerusalem, is a place yet to be built. The early saints often seemed to think that it was to be built in their time, and their attitudes often reflected this (sometimes to the offense of others who then owned the land), but this was not an official church view. However, it was revealed to the prophet Joseph Smith that Zion was to be in Jackson County, Missouri (on the American continent).
(not necessarily called Jerusalem)
There are many hymns about Jerusalem, but when used as a hymn title the reference is usually to the British quasi-patriotic hymn, adapted from a poem by William Blake, beginning "And Did Those Feet", customarily sung to the hymn tune Jerusalem composed by Charles Hubert Hastings Parry.