DMOZ or the Open Directory Project is web directory that has been around for a long time and is owned by AOL and run by volunteers as a hobby. They look for sites on the web and process sites that are submitted to categories to try and maintain a directory of the web. After submitting a site, it can take up to a few years before your site is reviewed and even then there is no guarantee of getting listed as they are very picky. The reason it takes so long is that there are more new website created every day than they can volunteers can process. It will only get worse.
There is a lot of misunderstand and misinformation about DMOZ. There is a lot of angst among webmasters about DMOZ, especially if they cannot get their site listed. There are lots of allegations of corruption at DMOZ and a lot of obsession about DMOZ at almost all webmaster forums. Most of it is unhealthy, non-productive and waste of time and energy.
The reason for that obsession is the mistaken belief that you cannot rank well in the search engines without a DMOZ listing. Plenty of sites rank well without a DMOZ listing. Having a listing in DMOZ is a nice link to have, but it is no more valuable that a similar link from any other site. It is not a search engine magic bullet.
DMOZ is what DMOZ is. Accept it. Submit your site once to the one best category and forget about it (there is plenty of good advice available). There is nothing more you or anyone can do. You either get listed or you don’t. Ignore the rhetoric and scuttlebutt. Spending time and energy on it is not worth it. Spend that time on energy on something worthwhile that actually makes a difference.