What is meant by "unless acted upon" in the Hadith: "Indeed, Allah has forgiven my nation for whatever thoughts cross their minds—or whatever they talk to themselves about—unless acted upon or spoken of," with illustrative examples?

One is not held accountable for inner thoughts unless they transform into actions performed by the limbs or words spoken by the tongue. A vow (nadhr) is among the verbal acts that necessarily require articulation; therefore, it is not concluded by mere inner thoughts.