What cause factions and why are they dangerous?

The danger of factions was discussed by James Madison in Federalist Paper #10. He defined a faction as a group of citizens who banded together with common goals, which if implemented would hurt the rights of other citizens or the community as a whole.
Madison writes that the cause of factionalism are inherent in human nature, because we can easily start to dislike others with different views, solely for those views. Furthermore, he writes that property ownership often creates these differing views as it divides society into groups along class lines. One example of this type of division is owners and renters. Owners want high property values and high rents and renters would prefer the opposite. This inherently sets these groups in opposition and this opposition can be inflamed into mutual dislike.
The grouping nature of factionalism is dangerous because it sets individuals in a country against each other. When this occurs, the interests of the majority will often infringe upon the rights of the minority. This leads to a situation the country is not ruled by law and is instead ruled by the whim of the people. This has historically lead to situations where the liberty, life or property is taken away from the minority. This stands in contrast to one of the generally recognized purposes of government: maintaining the rights of all for the public good.
Madison believed that the most pratical remedy for factionalism was to design the government as a republic, where citizens where represented by legislators. He also believed that this republic should have a large number of citizens with widely varied views. His hope was that the legislators could take the beliefs of the large number of citizens they represented and distill out of these beliefs the best path for the common good. In addition, he hoped that having a large number of citizens voting for each representative would reduce the likelihood that the representative had extreme views. However, this is only a bulwark against factionalism and does not stop it fully due to its strong roots in human nature.
FURTHER READING:
http://www.constitution.org/fed/federa10.htm

By faction, I am assuming you mean a division within a political movement or organization that splinters from a larger group to form its own independent one.
Based on this definition, there are several reasons why factions are formed. Within a movement, there are certain individuals who might disagree with one or more of the major values or policies, inspiring them to form their own group. They could also feel like they are not being listened to, which causes frustration and the desire to form a faction. They could also disagree not with the values of the primary group but with the methods by which it tries to achieve its goals.
To answer the second part of your question, I will discuss one of two ways in which factions can be dangerous. One reason why factions could be bad is that they can tarnish the unified message of the primary group, thereby creating obstacles to achieving the group’s goals. This means that movements could fail when multiple factions exist.
Another way factions can be dangerous is in the radicalization that often accompanies factions’ ideologies. Because a faction is comprised of more like-minded individuals than a larger group, it is more likely that radical opinions or methods will become platforms of the faction. This happens because insular groups lack the diverse perspectives that tend to moderate extreme opinions. As a result, factions within the government, for example, could cause civil unrest or use violence as a means to an end.