In the beginning, writers created motivation for their characters and, having done so, gave birth to stories.
Okay. Enough of the scriptural prelude.
While a lot can be said about characters and characterization, I would be remiss if I didn't start with the protagonist. Many people refer to the protagonist as the good guy, but I don't really believe in good or bad people, especially when it comes to literature. The best characters aren't stock or fill-in-the-blank characters; they are ones that make decisions that may or may not have adverse effects on others. It's kind of Zen-like when you think about it: characters define themselves by what they do. As such, a protagonist might best be described as simply "the main character," the character who enters the hero's journey or seeks to find something. And in keeping with the disposal of good and bad, the antagonist would simply be the character with a motivation that runs directly opposed to the motivation of the protagonist. These conflicting motivations give rise to conflict, which is what gives rise to plot (but that's another discussion altogether). *Note: Conflict is not just the effect of character on character motivation; it could arise from a number of factors, including nature, self, or a higher force.
If a character goes through changes, or is dynamic, he is considered round. That simply means that the character at the beginning of the story has evolved by the time the resolution comes. More than 90% of the protagonists in literature are round.
Flat characters are the opposite of round characters in that they are static and don't change. Hollywood tends to play with this type of character in movies that involve people with mental disabilities. While a mild argument could be placed on Raymond from Rain Man being round, he's actually much more of a flat character. As a result, flat characters tend to be accompanied by round characters. Just look at Forrest Gump. He had Jenny and Lieutenant Dan to balance him out. And Lenny had George in Steinbeck's novella Of Mice and Men.
Stock characters are best described as characters that, once they are seen, the reader automatically knows what role they serve. Just think of cowboys with white and black hats.
A final category of characters are archetypes, which, in the wrong hands, can become stereotypes. Each culture has its own archetypes. With African-American literature in particular, there are a number of them: the sambo, the mammy, the tragic mulatto, the bad-ass, the buck, the militant, the sapphire, and the list goes on and on. Just one look at a TV show like Good Times, and one sees many of these archetypes on full display. At one point in time, archetypes were original character types, but history has shown us that readers tend to respond to characters whose traits are recognizable in some way, so now archetypes straddle the line between being rehashed character types and stereotypes.
While a lot more could be said about characters, the main thing to remember is that they are representations of human beings (which is a pretty heavy notion when you think about it). Everything else is just a way of explaining how a character functions within a story.
Settings are more important than most novice writers might realize. While the most basic idea behind a setting is the "where" of the story, one particular type of setting must usually be addressed in literary (and even non-literary) stories: cultural/historical settings.
Each story actually comes out of a culture. There are numerous other cultural influences on the setting of a story, regardless of the writer's ethnicity. For example, Amy Tan's The Joy Luck Club comes out of the Chinese/Chinese-American culture. All writers draw from their cultures. Understanding this cultural component of a story helps to flesh out the background against which the plot is happening.
Now add in the historical element, or the period of time in which these events occur, and you have a more full setting. An examination of Alice Walker's The Color Purple clearly illustrates this. It's not just enough to know that you are dealing with a Southern, rural African-American culture; you have to also factor in the time period in which the events of the story are happening.
And why is any of this important?
It boils down to one word: Verisimilitude (a fancy word for "ringing true").
So you wouldn't see Miss Sophia running for the office of president of the United States, given the cultural/historic setting of the story, nor would a reader be able to appreciate the magnitude of the piano as a symbol in Amy Tan's story "Two Kinds," unless the reader could appreciate the cultural/historical elements that shape the conflict of the story.
While it's easy to just write a story and have the reader assume the cultural/historical elements of your setting, it is better to drop in a few references. After all, good writing should survive your lifetime, and if you want people to understand what you were talking about in your work, you have to frame it properly.