A visa that grants entry for some purpose on a temporary basis. As opposed to immigrant visas that can be converted to a green card.

After your study is over you're supposed to go home [0]. Generally when applying for a non-immigrant visa you want to show that you have a good reason to go back home. Otherwise you'll probably be denied.

Say I had an F1 and now it's long expired. Have a standard B1/B2 now. If I wish to immigrate to the US this doesn't help me in any way. Other than just being in good standing with them I guess.

[0] or you could get some other visa, but if you're coming in with this intent from the get go this is potentially problematic

I assume it is a visa that does not qualify one for naturalization after X years.

You are not expected to stay after the visa expires.

This definition is inaccurate.

Let me elaborate. No matter what type of visa you have, if you overstay, you will be out of status.

The difference between these visa types is that one can be used to apply for a change of status to permanent resident (green card) and the other does not.

If you want to get a green card and you have a non-immigrant visa, you have to apply to an immigrant visa first. There are exceptions but for temporary workers this is the case.