Negative SEO is basically when someone sends a ton of spammy, low quality backlinks to your site. The goal is to get Google to think your site is low quality because of all the crappy sites linking to you, and eventually devalue your site. There are actual companies that get paid to do negative SEO on behalf of their clients. It sucks, but it's reality.
However, this does not mean you cannot topple them. It just takes more of an effort in terms of content as your page has to build the trust. That is why you will see the "Google dance" happening for fresh content from a site that is not yet trusted or is not very authoritative. Google gives your page a chance and measures user click-throughs when it pushes you to certain spots in the SERPs and then measures user engagement levels when the traffic hit your site through those positions in the SERPs.