From Dictionary.com: Point of view: the position of the narrator in relation to the story, as indicated by the narrator's outlook from which the events are depicted and by the attitude toward the characters.
Two common POVs are first person (the "I" POV, where the narrator is a character, telling the story as it happened to him or her) and third person omniscient, where the narrator shifts perspective from one character to another, often within the same scene.
I like third person limited best.
Quoting from the Wikipedia article on point of view:
Third person limited is sometimes called the "over the shoulder" perspective; it shows the story as though the narrator could only describe events that could be perceived by a viewpoint character. ... However, some authors use an even narrower and more subjective perspective, as though the viewpoint character were narrating the story; this is dramatically very similar to the first person, allowing in-depth revelation of the protagonist's personality, but uses third-person grammar. ...
In third person limited the narrator is outside of the story and tells the story from only one character's view. The character's thoughts are revealed through the narrator. The reader learns the events of the narrative through the perceptions of the chosen character.
I like third person limited because it helps create the level of intimacy between reader and character that I want. First person might do that too, but I don't like to write it. I've only written one story in first person that I was happy with. (Thorns, the first short story I ever sold, to Realms of Fantasy back in 1995) I'm fine with reading books in first person POV, it's just not for me as a writer.
The big thing with point of view is that your viewpoint character can't know things unless she a) sees them herself or b) is told them by another character.
If your plot requires you to show the reader something that your viewpoint character (know hereafter as Sylvia) isn't present for, then you can switch to another viewpoint character for that scene or chapter. For example, chapter one is from Sylvia's perspective, chapter two from Fred's, etc. But Sylvia is still not going to know what happened to Fred in his chapter unless Sylvia was present or unless Fred or another character tells her. And even if Sylvia was present to see what happened to Fred, she still isn't going to know Fred's private thoughts, feelings, etc that were revealed to the reader from his viewpoint. Unless Sylvia is a telepath, she will have no more idea what Fred's thoughts are than you know what random passersby in the street are thinking. She can make guesses, which may be right or wrong, but that's it.
The basic mistake I seem to encounter most is that because the reader knows what the viewpoint characters have thought/done, the readers assumes that the viewpoint characters know it too. It doesn't work like that.
Obviously, in SF/F you can have telepathic or alien characters where you can play around with POV and do different things. And first person and third person limited are great for playing with unreliable narrators, where the viewpoint characters are either lying about the events they are experiencing or are perceiving events in a different way from the other characters.
Comments
Not sure that this will add too much to the discussion, but I participate in a few role-playing games and that mistake is one that we have to deal with in the games too. Because we, as the players know something, it's hard to remember that our characters don't necessarily know it. Some of the best writers have a horrible time writing a character in an RPG because they are unable to acquire that 'tunnel vision' you need to have.