It means that there is problem with the wi-fi connection to the Google servers. I think it replaces the older convention of an orange icon meaning no connection to the Google servers.
No connection to Google servers can mean one of two things--a problem with the overall web connection, or a problem with the Google servers. The latter can explain how people can still connect to websites, but just not with Google sites or apps(assuming they don't also have mobile data on).
No connection to Google servers can mean one of two things--a problem with the overall web connection, or a problem with the Google servers. The latter can explain how people can still connect to websites, but just not with Google sites or apps(assuming they don't also have mobile data on).