What is American Government Shutdown?? and How it will Affect us??

Satisfaction
Source for the following: A Senate staffer.
What is American Government Shutdown?? and How it will Affect us??

The United States government budgets money on an annual basis for a period of time called the "fiscal year." The government's fiscal year runs from October 1 - September 30. Every year before the fiscal year ends, Congress must pass appropriations bills funding all the agencies of the federal government in order to authorize them to spend money.
If agencies don't have authorization to spend money, it is illegal for them to carry out any non-essential activities that require spending money, which is pretty much everything.
(An aside: you can see all the different appropriations bills and their progress here.http://thomas.loc.gov/home/approp/app14.html)
On the one hand, this is a good process in theory. Every year Congress has to look at the programs in place and decide whether they're still worth funding at the old levels or whether something has changed and they should adjust funding levels.
On the other hand, it runs into practical problems. The government has grown a lot since this process was put into place and there's a lot more obstruction now than there was then, so most years this doesn't actually happen on time.
In order to deal with these delays, Congress tends to pass Continuing Resolutions (CR) to give itself some more time to work out the budgets of federal agencies it has not funded yet. A CR just says that whatever you had last year you get again this year, up to a certain date. So if last year your agency got $12 and this year we pass a 3 month CR, your agency will get $3 which it can spend over the next 3 months.
So that sets up the debate right now, which is not actually over whether or not to fund the government. No appropriations bills have passed, and Republicans and Democrats broadly agree that we should continue to fund the government for a few months while they work out their differences on appropriations bills.
The debate is about Obamacare. Republicans believe this is one of their last chances to repeal the law before it goes into effect. (The other one is the debt ceiling, which you've probably also heard about. They are related but distinct issues.)
As a result, some Republicans are refusing to vote to fund the government unless Obamacare is repealed/defunded. They believe that once the government is shut down, people will call on the Obama Administration to give in to Republican demands and start the government back up. Democrats and the Administration are unwilling to peel back their biggest achievement over the last five years to appease Republicans.
I should note that I'm on the Administration's side on this one. I think I've given a balanced view of what's going on while keeping this on an ELI5 level. If anyone takes issue with the way I've presented this, please say so and I'll edit this post or respond to your criticism.
Edit to respond to some FAQs:
How does this affect me right now?
The best overview of government services that are going to get immediately suspended that I've seen is from a post at Wonkblog. Some Some key points:
Housing: The Department of Housing and Urban Development will not be able to provide local housing authorities with additional money for housing vouchers. The nation's 3,300 public housing authorities will not receive payments, although most of these agencies, however, have funds to provide rental assistance through October.
Regulatory agencies: The Environmental Protection Agency will close down almost entirely during a shutdown, save for operations around Superfund cites. The Commodity Futures Trading Commission will also shut down. A few financial regulators, however, like the Securities and Exchange Commission, will remain open.
(Small parts of) Social Security: The Social Security Administration will keep on enough employees to make sure the checks keep going out. But the agency won't have enough staff to do things like help recipients replace their benefit cards or schedule new hearings for disability cases.
Veterans: Some key benefits will continue and the VA hospitals will remained open. But many services will be disrupted. The Veterans Benefits Administration will be unable to process education and rehabilitation benefits. The Board of Veterans' Appeals will be unable to hold hearings.
Does Congress keep getting paid?
Members of Congress do continue to get paid because it's unconstitutional to change their pay in the middle of a Congressional session. This is so they can't raise their own pay without giving the American people a chance to punish them for doing so. The way it's written, though, it covers decreases in wages as well so that's the way it is.
Staff are treated like all other federal government employees - they are not paid until the government is funded again. In the past, when the government was funded again, federal employees have been given back pay retroactively.
Are state/local government services effected?
This is a mixed bag. Anything funded purely through state and local funds should be unaffected unless money needs to be moved around to make up for a shortfall elsewhere. However, many state and local services are funded in part by the federal government, so you could see disruptions to a lot of services.