Arabs generally use only a first name. But you need to add other names so that you can be identified, I'll use Saddam Hussein as an example. In the Western world, you would assume that Hussein is the family name, but it is not. It is actually his father's first name. In fact, his entire name is Saddam Hussein al-Majid al-Tikriti, literally "Saddam, son of Hussein al-Majid, part of the al-Tikriti tribe". This is waaay too much for us westerners, so it becomes Saddam Hussein for our purposes. So Saddam is really his full name, the rest simply identifies which Saddam he is. So to call him "Mr. Hussein" would be incorrect, as it should simply be "Saddam".
Note that in this context, "al-Tikriti" might also be translated as "from the town of Tikrit" (literally, "the Tikriter," as one might say "New Yorker" or "Londoner"). You find something similar in the case of Abu Musab al-Zarqawi, who is from the town of Zarqa in Jordan.
Arabs don't just use patronyms as identifiers, by the way, but also filionyms (I suppose the word would be). "Abu Musab," to take the previous example, literally means "father of Musab," Musab being the guy's firstborn son. There's a certain amount of prestige attached to having fathered (or borne) a son, so the filionym is also an honorific (
kunya), and often takes precedence over the patronym. Mahmoud Abbas, of the Palestinian Authority, is also known as "Abu Mazen"; while a number of prominent PLO types used fictional (or, more charitably, metaphorical)
kunya as
noms de guerre, "Abu Mazen" actually is a filionym, after Abbas' eldest son.
In deciphering Arab names, "bin" or "ibn" means "son of," "bint" means "daughter of" (the British slang term "bint" for "girl" is derived from the Arabic, and was introduced by soldiers who'd served in Mesopotamia), "abu" means "father of" and "umm" means "mother of."