Less about the technique and more about the optics. Astroturfing is about building the perception of popular support. Bots pretending to be people can be astroturfing, but so can people putting up signs, people writing legislators, writing to newspaper, etc.
The idea is to make it look like support for/aversion to something is organic and popular (grassroots) when it's entirely artificial (astroturf)
More specific than that. You could describe blackmail like that.
The key characteristic of astroturfing is that it attempts to influence public opinion by presenting a false picture of the current public opinion. It's both of those things together that make something astroturfing.