Byzantine Iconoclasm was a period in the 8th and 9th centuries when intellectual discourse and political intrigue in the highest ecclesiastical and imperial circles was dominated by debate over whether icons (depictions of biblical scenes and figures that were meant to be venerated) and religious imagery in other artistic media constituted idolatry or served as intercessors to God.
One of this period's longest lasting effects was on the art historical remnants of the Byzantine Empire, which are relatively scarce in comparison to textual evidence of the grandeur of the empire. The major repercussion of the iconoclastic controversy was that the authority of the church in Constantinople over other sees became more of a formality than a reality.
Byzantine Ironclasm was two periods of Byzantine history when essentially there was a huge disagreement over whether or not it was ok for Religious Images to be used. Emperor Leo III actually for a time banned the use of imagery, as did a few of his successors. It caused a bigger East-West split, as well as the loss of Byzantine Italian territory. The early rise of Ironclasm can be attributed to the rise of Islam, which also viewed such imagery abhorrently.
Sources: A Short History of Byzantium by John Julius Norwich