These are keywords (or matched search terms) the domain has advertised on at any time. Any keywords that we list (as a paid keyword) have triggered the domain's ad somewhere on the first 2 pages of the SERP at least once.
It is possible that the domain did not choose to advertise on the exact keyword shown, but because of match types and Google's ad match settings, the ad appeared. You can verify any ad claim using our cached screen shot pages for every SERP.