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.
Note - at this point Google already has baseline metrics from other search results. So, if your site beats them by a factor of say 3x then Google thinks - hey.. this page looks to be way better - so why not stick its rankings in the long term and why not even bounce it up higher and see what happens and measure again how users engage with the site?
Of all the tools listed in this article, Moz Link explorer is an old one & quite popular. If you want to compare backlinks between two or more domains, Open Site Explorer is worth trying. This tool works best when you have a paid account of SEOMOZ though a free version of this tool is good enough to get you started checking the backlinks of your site and the sites of your competitors.