Broadly speaking, UNIX is a family of Operating systems arising from the original developed by AT&T in 1969. Over time, UNIX has split into multiple branches with a wide range of applications within the Server Arena.
Whilst not UNIX in it's true form, the Open Source Operating System GNU/Linux is based around the concepts of UNIX and operates in much the same way. Operating systems such as FreeBSD (from which Apple's Mac OS/X is derived) are also considered UNIX Compliant.
For a Joomla! administrator, the nuances of managing a UNIX system are not that important. Given that most Joomla! site's will probably be hosted on a UNIX compliant system, it would be wise to understand how the permissions system works as incorrect settings can lead to Joomla! not functioning correctly (usually by preventing you from installing extensions or uploading media, but with particularly poorly configured permissions Joomla! may not run at all!). Here is more about file permissions for Joomla!
At the file/directory level UNIX based systems assign permissions to three categories of user:
These permissions are usually represented by three numbers (e.g. 755).
Owner permissions should be self explanatory, although it should be noted that the owner will not necessarily be the user who created the file.
Users can be added to any number of groups, and assigning permissions to a group will allow all users within that group to complete the permitted actions. This allows a system administrator to allow certain permissions to certain users without needing to indiscriminately allow for all.
Everyone should, again, be fairly self-explanatory. This specifies the permissions allowed to any user (it's considered very bad practice to allow write permissions to all without good reason).
Each permission is usually represented with a numeral, below is what each denotes
Generally you'll not come across a permission setting lower than 4, as the practical use of 0 - 3 is somewhat limited.
As an example, to allow the owner to read/write and others to simply read we'd want the permissions for our file to be 655.
The best way to learn, however, is often to download, install and use a UNIX based OS for a while!