What would it mean for a news source to be neutral?

We occasionally have questions here that ask about neutral news sources, and there is no shortage of opinions about what sources are the most “neutral”. But what exactly could this mean? Is this even possible?

The selection of events to be discussed, the information that is mentioned as relevant, and nearly everything about reporting on something seems impossible to separate from the bias/preference of the people and/or organization doing the reporting.

How do you come to the conclusion that a news source is “neutral”? And what is a good example of a neutral report?