I’m working on a website and am pulling category names from a db table (category_names). I then display them on the website using php on to an html unordered list. I want to limit the number of category_names and then using jquery(or anything else but I prefer jQuery) retrieve more category_names and add a less button to go back.

I hope I made this question easy to understand, and thank you for any help!
There are a number of different approaches that work better or worse depending upon your needs.
Approach 1 (simpler, less efficient, scales poorly): execute the full query, and store all of the results on the DOM, just hiding them using jQuery (jQuery expander is a simple plugin you may want to try out, though I have found it limiting in customization).
Approach 2 (more complicated, but more efficient/scalable, also faster): Use MySQL limit, you can actually send a second mysql request on click, however, you would want to make sure this is asynchronous so as to not delay the user’s interactions.
http://php.about.com/od/mysqlcommands/g/Limit_sql.htm
This is similar to: PHP/MySQL Show first X results, hide the rest