What does voice in writing mean?

What does it mean when people talk about voice when referring to someone's writing? Is it his/her specific point of view? or Can two people have the same point of view and different writing voices?

In terms of writing, "voice" can mean several different things, depending on unpredictable variables.

1. It can mean "point of view", as Matthew points out. This is a visual metaphor
2. It can also mean "agency or lack of agency", in a metaphor with the Latin (Inflected) Passive Voice (which does not exist in English). This is a grammatical metaphor.
3. It can also mean — and this is the way I use it, at least, in writing about writing — the imagined voice of the author that the reader hears in their Mind's Ear as they go along. I read Terry Pratchett's books, for example, in what I fondly hope is a Buckinghamshire/Somerset accent. And I hear commas as intonation curves. This is an auditory metaphor.

Clearly, not everybody reads the same way. Literacy is modern technology — not naturally-evolved like real language — and not everybody realizes yet that writing is just transcribed speech — i.e, "voice". Everybody, as we all know, develops their own ways of dealing with technology, and writing is no exception.

Thus, I'm certain that I'm missing some senses. But the metaphor is clear:

WRITING is SPEAKING

[Written] Voice: An author’s unique style and way of saying things. You should be able to recognize an author’s written voice the way you recognize a person’s spoken voice. In creative writing, one goal is to develop your written voice. Your voice should come across as natural, clear, and consistent, as unique to you as a fingerprint. Wordiness, awkward use of language, awkward sentence structure, and lack of clarity all serve to muffle the voice of the author.

In writing as in speech, "voice" is about how you express yourself - style, rather than substance.

A writer's "point of view" on any specific subject isn't necessarily relevant to how he expresses his views. If Ernest Hemmingway had ever changed his opinion about bullfighting and decided to disparage it, any such writing would still embody his distinctive "written voice" (characterised by short precise phrasing, omission of peripheral details, etc.).

Usually 'voice' means the 'point of view' that the prose is meant to convey.

So, for example, 'stream-of-consciousness voice' is meant to give you the thoughts of (usually) the narrator, from moment to moment. 'Character voice' is meant to convey that this is one person's (i.e. "character's") version of a story, where the character may or may not be central to the plot unfolding.