And I preface this by acknowledging that it's a gross mistake to characterize Arabs in such a monolithic manner but you can't escape the fact that the Western media does by and large treat them that way.
Anyway you often hear, in the news, when discussing conflicts in Iraq or Libya, about the various conflicts between so-called 'tribes' or 'clans' which seem to take precedence over other forms of political allegiance. It's never clarified what that actually means. Is tribe or clan allegiance based on familial connections? Geographic proximity? A relic of past nomadic groupings? What are they and what makes them such a prominent feature of Arab politics? Why have they not been wholly subsumed by other political identities based on concepts of religion or nationhood or ethnicity or civic ideologies like in other parts of the world?
This probably won't be very informative for you, but I can give you some insight on modern tribal societies in northern Iraq, Syria and Turkey. May be it will be useful.
A modern "tribe" in both Turkey and neighboring areas(northern Iraq and Syria) is not actually what you would presume based on actual tribalism. The word "aşiret", which is probably Arabic in origin, is used to describe such groups, and they are essentially gigantic families more than anything. The majority of an Arab clan, or a Kurdish clan, are often related to each other in some way.
While the origins of Turkmen aşirets can be traced back to very old(like really, really old) nomadic roots, and familial ties are less important than shared history and culture; Kurds and Arabs of Iraqi Kurdistan use a system based on both feodal tradition and kinship. Often enough, you can find a clan that use a fairly recent "common ancestor" name as identification. Anatolian Kurds in particular, still have clans that owe fealty to an "Agha", which is Turkish for feodal lord.
As for why they are still a thing, I could talk about Kurds and Turkmens, but I'm afraid my limited knowledge ends there for Arab people.