Astroturfing is the practice of really praising something (e.g. a new ICO), without also revealing that you have a personal interest in the relevant product/service. For instance, it is common that people behind an ICO go out on forums such as Bitcointalk.org and give a lot of credit to such ICO. This is to make it seem that the crypto community as a whole is in favor of the project.
Astroturf in the “normal world” is the brand name of a specific type of fake grass launched by Southwest Recreational Industries, Inc. (patented in 1967).