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It's a directory edited by volunteer editors and, although it's not well known to new net users (like Yahoo is), it is one of the more important places to be listed. ODP results have been included in AOL Search for some time, and are currently included in Google results and many other leading SEs. I'm told an SE can use ODP's information at no cost. That and the high quality have contributed to it's continuing popularity.
>I can tell you a little, though others will have to help with the history... ODP is the Open Directory Project and can be found at dmoz.org
As for history, there is a fairly lengthy history available here [laisha.com], although it was written last year and so, of course, stops then.
It is important because all these sites use their data. [dmoz.org]