Google (or Bing) AdWords is an online advertising web service, where you can promote your website. It is Pay Per Click system.
Paid AdWords are always displaying above regular search results and on the right sidebar.
It is essential to have Google AdWords if you are just starting your business or your website and it is a lot of competitors. If you are just "attacking" smaller areas, like one town (local businesses) Google AdWords are not essential, as SEO should be enough, but it is still useful.