Turns out that it wasn't entirely, or even mostly. Erdogan's call that did it. The mosques turned on their call-to-prayer PA systems and ordered their followers into the streets.
Also, not all people protesting on the streets are protesting for Erdogan, lots of them are simply protesting against a military coup that is trying to overthrow an elected government (whether they like this particular government or not).
While it sounds like a joke coming from Erdogan, with his "ambivalent" relationship to democracy, asking the people to go to the squares and streets is asking them to defend a democracy.
Sadly, either outcome still leaves Turkey less democratic and less stable than before. As it currently seems, Erdogan is going to have more power than ever before with all his adversaries purged from the military.
Such is the way of leaders throughout history. For instance, Rev. Dr. King deliberately had teenagers get assaulted with dogs, water cannon, and truncheons as a tactic for getting media attention.
Hmmm, it occurs to me that I don't actually have a good introductory source for someone new to learning about the US civil rights movement of the 50s/60s.
[1] http://www.telegraph.co.uk/news/2016/07/15/turkey-low-flying...