Problems with server permissions sometimes occurs among PHP applications (such as Wordpress) that needs to write to the server.   There are many possible causes that may produce similiar permission errors such as "unable to create directory" or not being able to upload images, etc.  So a solution for one case may not work for another similar case.

The first thing to understand is how Apache server permission works and how Wordpress relies on the settings of these permission in order to work completely.  Linked here is good overview of permissions. Note especially the potential dangers of 777.

Once you got a good understanding of the problem, do a web search using keywords from your error message.  I'm sure you will find tons of results.  Here are some threads from the Wordpress forums that talks about such permission problems in Wordpress: 1, 2.  Hopefully some of the solutions described in the thread would work.