I believe that term comes from no less an authority than David Axelrod, of Obama White House Fame.
It is a term he uses when he gins up phony baloney crowds to make it look like they really care about something - but are instead shills he has gathered and paid through his organization for his clients. Think, SEIU or ACORN thugs with professionally made signs who are paid to show up and are let in early and given the best seats in the house.
Leftists like Pelosi are accusing anti-DeathCare people of being Astroturf bought and paid for by insurance companies and the GOP rather than spontaneous individuals motivated and acting by themselves.
"Astroturfing" is the Liberal's own tactic and name for it, and they can't imagine anybody demonstrating for/against something unless they are organized, bussed, and paid by a special interest group to do it.
Why? Because that is what they do and how they get their highly organized crowds to show up.
Amen.......preach it.