The particular eight-pointed star (or octogram) pictured here is unusual in that it has multiple meanings, depending on context. The original emblem of two overlapping squares, often with a circular ornament, is called a rub el hisb (Arabic, quarter-group), an ornament used to mark the end of passages in the Q’uran. This symbol, like all symbols related to Islam, is not official nor heavily symbolic.
An identical glyph serves as the emblem of the Melchizedek priesthood of the Church of Latter-Day Saints, who view it as a continuation of the priesthood of biblical patriarchs. The emblem is patterned after a similar glyph found in a medieval depiction of Melchizedek, but is of relatively recent usage in Mormonism. The star in this context would most likely have been a symbol of renewal and rebirth through baptism.
A mosaic illustration of Melchizedek with eight-pointed star
A Mormon commemorative badge
Decorated Roub al Hizb from the arms of Turkmenistan