What does "Site to add the smart computer group to" do?

So, think of a site like a subdivision. If you have a default site set as A, you will only get machines that are listed to belong with site A. By setting the site to "none", you're including ALL subdivisions (sites). Basically, a designation of no site means all sites are taken into account.

I think I got the concept of a site, what confuses me is the impact or consequence of the "Site to add the smart computer group to". Does it

1) add computers to a site;
2) make a smart group visible in a given site only, 3) apply the criteria only to computers in a give site (in that case I find there is plenty of room for improving the phrasing).

So you think 3) is the correct answer?

A Smart Group that has been explicitly added to a Site will calculate/include devices that are already assigned to this Site only. By contrast, a Smart Group that is not assigned to a site (by leaving the option set to "none") will include clients from anywhere in the JSS, whether assigned to a Site or not.

This allows you to compartmentalise your environment into smaller, self-contained, instances as the same logic applies to most other relationships. For example, a user assigned to "Site A" can only see the corresponding Smart/Static Groups, configuration profiles, policies, clients, DEP instances, VPP accounts etc that exist in "Site A". While a user assigned to "Site B" would not be able to see any of the above unless given explicit access. Finally, a user that is assigned "Full Access" has visibility over the entire JSS and across sites.

I hope this helps!

So, @mschroder your answers 2 and 3 are both correct.