Historical background: This verse provides critical time and culture grounding for our understanding of the Book of Mormon. In the first case, it provides us an opportunity to place a date on the beginning of the Book of Mormon events. All we need to do is find out the year which corresponds to the first year of the reign of Zedekiah. Scholars provide that date as 597 BC. This date falls among several turbulent years for Judah. Judah was caught (not untypically) between Egypt and Babylonia. The following information covers the years from 609-597 BC).
"Egypt immediately claimed Judah as a dependency and put Jehoiakim on the throne as vassal. Subsequently, when Neo-Babylonia drove Egypt out of Canaan, Jehoiakim shifted his allegiance to Nebuchadnezzar II, but then revolted at the first opportunity. In a retaliatory campaign, Nebuchadnezzar captured Jerusalem and deported his son Jehoiachin (perhaps after his father's assassination?), along with a sizable group of government officials. Zedekiah was installed as a vassal regent, Jehoiachin retaining the status of king in the eyes of the Neo-Babylonians and most Judahites. After more anti-Babylonian machination, relying on promised Egyptian support that fizzled, another revolt by Judah was crushed - this time with the baleful result of the destruction of Jerusalem and its temple, further deportations of leaders, and the cessation of the independent Kingdom of Judah." (Norman K. Gottwald The Hebrew Bible . Fortress Press 1985:372).
As most Book of Mormon chronology centers around this date (the only other externally fixed date being the birth/death of Christ) it is important to understand that all other dates in the Book of Mormon are educated reconstructions based on those two fixed points. An excellent discussion of Book of Mormon dating is Randall P. Spackman's "Introduction to Book of Mormon Chronology" (FARMS 1993). It is important, however, to remember that all other dating is only approximate, even though models can be built which give the general outline of Book of Mormon chronology.
Religious significance: From the standpoint of LDS understanding of the scriptures, the second part of the verse is interesting. Many prophets entered Jerusalem to prophesy of the impending destruction of Jerusalem, which did eventually occur. The modern LDS term "Prophet" stands for a particular position in the church, and carries with it the stated injunction that there will only be one Prophet for the church at any given time. Many of us learn that so well that we forget that the twelve are also prophets. In like manner, ancient Israel had prophets with revelatory functions, but not necessarily leadership roles. It would be highly unlikely if any of the prophets prophesying at that time in Jerusalem had actually been part of the officially recognized religions governing bodies. Lehi's call to a be a prophet followed in that tradition. He was not unique in his calling as a prophet - he was one of many. In fact, Jeremiah would have been one of his contemporaries.