To whom is title "Professor Emeritus" given in the US?

In the U.S., "professor emeritus" simply means "retired professor". It's a courtesy title offered to retiring professors to acknowledge their continued scholarly role even after formal retirement. It typically includes library privileges and a computer account, and emeritus professors may also have offices (this depends on departmental policy and the availability of space). It's sometimes possible to teach, but this is a special arrangement rather than a job requirement.

At many universities every retired faculty member is offered this title, with rare exceptions for people who committed misconduct or angered the administration. At other universities one has to apply for the title and make a case for why it is justified.

In particular, professor emeritus is not a higher title or special distinction. It can be viewed as a retirement incentive: even after retirement, you'll still have a respected role as well as necessities like library access. However, there's no advantage to becoming an emeritus professor beyond the benefits of retiring from your job (i.e., giving up duties and focusing only on what you prefer).

Professor Emeritus is essentially a form of retirement for academics.

Departments typically have a tightly constrained number of faculty slots. When a tenured professor is either not interested or becoming physically incapable of fulfilling all of the expected duties of a full-time faculty member, they may move (or in some cases be involuntarily moved) to emeritus status. That opens up a faculty slot for a new hire without severing the relationship of the old professor with the department. Typically, emeritus professors still have many rights and opportunities to participate and contribute: some still teach, supervise students, raise money, etc., such that they are practically still a full faculty member, while others just turn up occasionally to say hello.

The others already made the basics clear (em. = retired), but I would like to add that the actual meaning of the title largely depends on the institution. I have been to the University of Zurich and there it is basically just a formality with no privileges attached to the title. However, at my current institution the Prof. em. remains head of the faculty, theoretically until his death (many withdraw voluntarily much earlier). They continue lecturing and have office hours the days they are present. Many also continue supervising final theses, though this is normally limited to the higher level ones, like dissertations, not master's or even bachelor's theses anymore.

The word itself stems from "emereri", meaning "earning a privilege", but - interestingly... - also "becoming useless". The latter has been used for soldiers in the Roman army, when they were not fit for service anymore and later was applied on many other branches. In German speaking regions it's e.g. often the case that retired lawyers are adressed as "emeritus" by their former partners.