Is it possible, and how can I go about this?
Yes, but with ajax help and server side script. jquery and JS doesn't support MySQL connection.
Not directly but you can use Ajax to fetch content from a page generated by a server side language. Here is how to use Ajax with jQuery.
Short answer:
No, you can't do that out of the box. JavaScript code runs in the browser, the MySQL-Database on the server. Browser-Javascript cannot run any code directly on the server (pfewww! :).
Long answer:
Some Web-Development-Frameworks expose the underlying database-structure in a well-defined (sometimes RESTful) manner in json:
In case of a hypothetical model 'User' in Ruby on Rails:
The list of all users, when issued as GET request. Creates a new User, when issued as POST.
/users.json
Returns the User with the database-id 1, when issued as GET request. Updates the User with database-id 1 when issued as PUT-Request. Removes the object when issued as DELETE request.
/users/1.json
The returned json-code (JavaScript Object Notation) can easily be parsed using eval() in JavaScript. So here's a way to access your database using jQuery in semi-direct way :)
Hope this helps