What do we mean by “nonexcludable” and “nonrival” when talking about public goods? Public goods challenge markets because it’s difficult to charge non-payers and it

What do we mean by “nonexcludable” and “nonrival” when talking about public goods? Public goods challenge markets because it’s difficult to charge non-payers and it’s inefficient to exclude anyone — so, how do we produce them? Public goods provide an argument for taxation and government provision. But how do we know which public goods should be provided? In this video we cover the free-rider problem and the forced-rider problem in regards to public goods. We also discuss examples of the four different categories of goods which will be covered in future videos: private goods, commons resources, club goods, and public goods.

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Health care is a name for many kinds of services, some of which are private goods, some of which have public goods features. Many goods under the heading health care are private goods, such as an aspirin for my headache or a surgical intervention to fix my broken leg are private. But vaccines against contagious diseases are goods with public goods features. They pose a problem for markets.
Imagine we are colleagues working in the same office and you don't know if you should get the vaccine for you or not. If you get the shot, then you also protect me. If you get the shot, you cannot exclude me from benefitting from a safe environment at work, which you created by having it yourself. Neither am I preventing you from staying healthy just by being there at work and enjoying that protection. Since the shot is expensive, you might want to wait for me to have the shot and protect you as a side effect. We both want to free ride on the other, so it is possible that neither of us gets it. We might then get sick.
However, the fact that a public good poses a problem for markets does not mean that markets cannot anticipate and prevent that problem. Our employer competes with other employers. She cannot afford the risk of having us both sick. To prevent this problem she makes a proviso in our employment contract whereby at the beginning of the cold season one of us is randomly drawn to have the flu shot, while we both take equal cuts from our paychecks to cover the cost of that one shot. The flu shot is still a public good, but no taxation was needed to pay for it. We voluntarily agreed to work for this company under this proviso.
The type of solution here is called a tied sale. Our employer tied a condition (a cost to us) to the job offer (which is otherwise a benefit to us). She sold us the entire package.

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Ah. I see. In the following video, wi-fi bandwidth is called nonrival, "assuming no congestion". Yosemite is nonrival if we likewise assume no congestion.

Exactly right!

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Non Rival: one person using the goods does not prevent others from using the goods at the same time which applies to both the national park and wifi.

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