I am trying to reduce the time taken to download my website. I purchased a template and this is always loaded on every page. Do I really need it? To see the delay problems the link is www.drachsi.com Drachsi
I can't see any delay problem. Anyway... jQuery is a javascript library that allows to write "complex" stuff more easily. In your case, you have "index-script.js" that depends on jQuery library. So its ok.
upon checking on your website with YSlow, in which your website's grade is F, jquery is not your problem with regards of loading time of your website. you have a lot of external css and js. try to install YSlow and it will guide you with what to do in increasing your site's performance.