. . . information regarding 2013 Directories List and how they are useful to us.
That is a wide open question.
1) How are they are useful? If you don't already know, why are you asking for them? Especially if you are into SEO?!
2) Are you looking for a ready-made list of directories announced in 2013? We are only 2 months into the year, so it will probably be a rather short list. I doubt a list like that has been compiled yet, but if you want to keep an eye open for the latest directories as they are announced you are better off in a forum specifically about SEO (e.g. - SP, DP, V7N, IVS, etc.).
3) I wouldn't waste time on directory submission. It used to be a method of SEO, but it is all but pointless now. Google has devalued directory submission a lot, and I hope they keep doing so. Hopefully, soon it will be completely devalued and all these useless directories can disappear and stop polluting the Internet.