As the commenter pointed out - you're missing jQuery from the fiddle which is why it doesn't work.
jQuery comes with 2 different easing options out of the box, swing (the default) and linear which as the name suggests is constant.
However, there's a really good library for different easing options that you can plug in - there's a link here and you can try out the different kinds on the page. Download it, include it in your website (after jQuery) and you can use the different easing methods.
To use easing in your code just add the type of easing after the duration. E.g.
$("#element").animate({"left":0},1000,"easingName");