So why are they considered to be so important?
Important is not the right word.
The fact is they are the oldest general web directories. Yahoo was the first way to find a web site since it was launched in 1994 before any search engine. DMOZ was launched several years later (in 1998, just the year when google was incorporated).
the Open Source Directory
As for the potential benefits of a listing in DMOZ, a major change occurred last year. Before 2011, the DMOZ data base was fully duplicated into the Google directory: the latter was a high PR directory and it was pretty well ranked in the SERPs. Since mid-2011, Google directory has been closed. This reduces considerably the possible benefits of a listing in DMOZ.
Some people may also consider that the end of google's partnership may lead sooner or later to the end of DMOZ.