Negative Keywords help prevent unwanted click-throughs.
If you run a pizza delivery restaurant in Littleton, CO, you probably don't want calls from Aurora, Colorado. They waste time with inquiries from people outside of your business area, and you'll pay for click-throughs from non-customers.
By adding towns not in your delivery area as "negative keywords," Search Engines won't display your ads for search terms with these towns in the search query.
Another common use of negative keywords is sorting sub-categories of business: For example, Auto Repair and Auto Sales. As a mechanic, you don't want to pay for click-throughs by customers looking to purchase a new car.
In addition to directly saving money, Negative Keywords help improve your Quality Score and improve the placement of your ads.
Reviewing Search Terms resulting in Click-Throughs to your site helps can help find negative keywords. For example, in a hypothetical pizza restaurant, you might find some click-throughs were generated from searches for pizza cooking instructions. You'd probably want to add those terms (and others closely related) to a negative keyword list.