A Denomination means a subset of a larger group, usually pertaining to religion. Denominations were created mainly when a group of people felt or thought differently than everyone else they worshipped with, and so they split off and start their own church.
Martin Luther, for example, after reading the Bible, interpreted contemporary practices of the Roman Catholic Church as inconsistent with God's Word. After being excommunicated he started his own denomination based on his interpretation of the Bible.
Those that belong to an older denomination say the newer, "daughter" denomintations are sheep that have gone astray from the fundamental truth. Espousers of the new denomintations say that, through the years the old church got away from the truth and relied more on tradition. They start a new church to get back to the fundamental truths. Different denominations are the product of different interpretations.
Cults arise when people take scripture out of context, when people make up their own ideas, or when they don't like the ideas they've heard in other places.
All religions have different denominations, generally because one believes all the others are fatally wrong. Each person has his own soul, and the freedom to think what he wants; very few people are in exact agreement about everything.