Essential services like police and hospitals aren't shut down. Social security, military payments, and stuff like that is still funded because that comes from a different fund. Pretty sure the IRS keeps working too.
Other than that all federal employees basically get a free paid vacation because once the government starts back up again they'll receive pay for all of the days they were furloughed, the only catch being they have to make do without receiving a paycheck until then.
I think a government shutdown is more psychological to people than anything else because "government shutdown" sounds ominous and they don't understand exactly what it entails
Also parks typically aren't closed during a government shutdown, that was just Obama's doing to make Republicans look bad. Why would a park or a veteran memorial need to be shut down just because the federal government is temporarily shut down? It's a park, it's not Fort Knox.