It's to stop your ad from showing to searchers you don't want - the most obvious one is to have 'free' as a negative, if you're selling something, as you don't want loads of people clicking your stuff who are specifically looking for free stuff.
Basically, negative keywords are used to improve your ad campaign. This helps you to refine search. If you don't want to show your ads on some specific keywords or words than add it and put (-) sign before it. Ex: - free trail. Your ad will not show on these type of keyword search.