To have more than a cursory understanding of the region, it is critical to possess at least a basic knowledge of the Sunni-Shia split within Islam. The Sunni-Shia rivalry goes back 1,400 years, and in a nutshell involves the different sects beliefs about who was the legitimate successor to the Prophet Muhammad after his death in 632 AD in what is now Saudi Arabia. In a nutshell, one group of the Prophet's followers believed the next ruler - the Caliph - should be chosen by the community of Muslims as best able to represent the new faith. The Shia, by contrast, believed that the leader of Islam should stay within the Prophet's family, and they favored the Prophet's cousin and son-in-law Ali as the next Caliph.
After some initial turmoil in which a number of the early caliphs were killed, Ali became the fourth caliph but not before war broke-out between the Sunnis and Shia, and Ali was killed by Sunni forces. Ali's son Hussein took over leadership of the Shia branch from Ali, and eventually faced a huge Sunni army led by a Sunni caliph. Hussein and a large part of family were slaughtered by the Sunni forces in battle, and Hussein's head was decapitated after his death. Ever since then, Shiites have seen Hussein as a martyr unjustly killed by Sunni forces, and as a result the Shia philosophy revolves around maryrdom and suffering. On the anniversary of Hussein's death, Shia frequently beat their chests and cry out the name of Hussein, and some even flagellate themselves. Sunni extremists, meanwhile, see the Shiites as heretics, and believe they have deviated from what is true Islam. For those interested in a good overview of the Sunni-Shia history and divide, I highly recommend a series of short pieces from NPR:
Origins of the Sunni-Shia Split
Key Figures in the Sunni-Shia Divide
Chronology in the Sunni-Shia Divide
Shia Rise in the 20th Century