Out of the loop

I would note that the USA is about the only place this is actually possible.

In pretty much all other democracies, if the parliament fails to pass the budget bill, it triggers a dissolution of both houses and an election is held.

It's an unfortunately common, bullshit move politicians pull, just to have something to hang over each other's heads in order to get what they want. Unfortunately, that has become totally ok in the eyes of Republican voters because it's often the only way for their reps to force through budget items that would otherwise never make it.

Mom gives you a weekly grocery list with $50 worth of products on it. You must buy everything on it every week.

Mom tells you to take $150 out of her wallet every month. You may not take any more.

You know you'll be short. She knows you'll be short. But you can get by for three weeks, so she'll wait until then to address the issue.

as @Travalaaaaaaanche! mentioned, it’s just a form of brinksmanship – they don’t care “how it affects people” so long as they get their way

Congress is supposed to decide yearly on how and where money gets spent in the federal government budget. If they do not pass the budget before the old one expires, the federal government cannot spend any more money, and it's operations immediately cease.

The political factions of Congress get into pretty regular spats over how the money is spent, either because not enough is going towards projects certain factions want, or too much is going towards projects that other factions are staunchly opposed to. Sometimes unrelated law bills get tacked to the side that become a point of contention too. With politics becoming more and more polarized, they reach deadlock and can't agree on the budget, and bam, you get a shutdown.

The same goes for the artificial "debt ceiling" Congress imposed upon themselves that limits how much money the government can borrow from... well, itself, basically. When they hit the cap they also cannot continue spending, so it has to be regularly increased (achieving absolutely nothing)

Either/both sides can and will try to threaten a shutdown as a bargaining chip to get what they want, but it's so overused at this point that it really doesn't help much. They still run right to the end, pass some temporary in-situ funding agreements, continue the deadlock, then go back to massive deficit spending at the end of the day anyway.

The government shuts down when there's no budget passed by Congress authorizing the money to keep it open. This isn't a good thing but happens when Congress can't get it's act straight. Crazy Republicans from deep red districts are making basic governing impossible, like passing a budget.

Republicans breaking the give to own the libs

Because congress has totally abdicated their constitutional duties - read it - this is not how our government works - this is an inexorably broken government - both sides.