You know perfectly well what they mean - inserting a gene from something totally unrelated into an organism, as opposed to ordinary selective breeding.
What is ordinary about selective breeding?
This is the problem, they don't understand the science, if they did they would have been more careful of their definition.
The problem is that they are condemning a general technique instead of looking at the results on a case by case basis. Can GMO products be dangerous? Yes. In one case when they spliced a certain gene from a peanut plant into soya in order to improve the soya crop, they found the resulting soya beans could trigger peanut allergies. That particular avenue was quickly dropped. However, in other cases, GMO crops have proven beneficial. For example, if you breed a crop that needs less insecticide, that's a good thing right? Fewer chemicals sprayed throughout the countryside must be good.
Blindly opposing GMO just for the sake of opposing GMO is stupid. It's like opposing the manufacture of all drugs because sometimes you get bad drugs out like thalidomide or heroin.
