Dynamic Characters are characters that change (internally, not necessarily physically) in the course of the story, generally as a result of a lesson they've learned, some insight they've developed, or a truth they've discovered. This path of change is called a character arc. When one explores how and why--especially why--a character changes during the course of a story, and discovers the lesson (or whatever) that underlies the change, then typically he/she has discovered the theme, what the story is about.
Static Characters are characters that remain essentially unchanged internally from the beginning of the story to the end. Action/adventure stories often have main characters who are static (although having a static main character does not necessarily make a story an "action/adventure" story). Over the course of the story, such characters change their environment but do not change themselves.
Stories which have static main characters are sometimes said to be "plot-driven," while stories where the main character is dynamic and a theme results are said to be "character-driven."
In the short story, "The Smuggler," by Victor Canning, both The Great Man and Tasso are static characters
In the short story, "Split Cherry Tree," by Jesse Stuart, the character, Dave, is dynamic.
In character-driven stories where theme is important, there may still be static characters; he/they just won't be the main character(s). It is also possible that in a story where the main character does not change, that minor characters might.
"Round" characters are characters which the author develops in some detail rendering them unique and making them seem very human; "flat" characters (the idea suggesting the cardboard cutouts of star photos propped up in movie theater lobbies) are characters the writer has brought to life with a minimum of detail, and which probably rely to some degree on notions of such people already in our brains (stereotypes).
Stock characters result from generalized ideas about types of people that our brains have assembled from a few shared characteristics of such people. The English butler, the western gunfighter, and so on. These characters are not unique in any way, but project only (or primarily) characteristics of the group to which they belong. It is accurate to call these stock characters stereotypes but the term "stereotype," as many people use it, implies the assumption of certain values, attitudes, capabilities, and so on (like "dumb blonde") which is not true for all stock characters. Use of stock or stereotypical characters can be a useful shortcut for writers in creating characters of little importance, but an undesirable alternative when creating characters that should have been developed in greater detail--and thereby made more unique.
Characterization is any writing which tends to manifest a character in the mind of the reader. Good writers have always seemed to understand (even if they couldn't consciously explain it) that what people say and do reveals more about them than how they look, although before the advent of modern psychology, writers in general tended to rely more on description of characters to establish who they were than they do now. But today it is uncommon for a writer to rely much on description, except to reveal characteristics like, race, gender, size, strength, or age--if these qualities are important. Action, what characters do, is generally the most powerful indicator of who and what a character is, followed by dialogue. But characters are revealed not not just by what they say (or don't say), but by who they're saying it to and who they're saying it about. Even more revealing sometimes is what others say to them and about them. By the same token, a character's reaction both to environmental stimuli and to other characters is perhaps more revealing than deliberate actions that he takes. An important character that recurs in a story is often given a character tag, a unique way of doing something, or saying something, or a unique physical characteristic. Whenever it comes up in the story, we will automatically associate it with that character. A character may have a limp, or an accent, or smoke a cigar; he may mispronounce a word, or always wear a certain kind of hat. Then, lets say, we see a shadow of a man in a certain kind of hat, smoking a cigar--the character the writer wants us to think of is going to immediately spring into our minds--even if that's a wrong guess (Sometimes writers lead us to expect one thing, but surprise us with another.).
The main character in a story or novel is usually a protagonist, that is someone who is trying to solve a problem or accomplish a goal. Frequently the main character is also the point-of-view character, the one through whose eyes, or over whose shoulder, we perceive the events of the story. When such a point of view is used, there is usually a tendency for the reader to identify with the main character, regardless of his/her gender, and to sympathize with him, regardless of whether the character is good or evil. While writers tend to take advantage of this relationship between reader and main character to force readers to examine certain ideas or issues, which may or may not be relevant to the main theme, the reader/main character relationship always provides a unique angle on the main theme, too.
Today, any character who opposes a protagonist might properly be called an antagonist, whether that opposition is direct and substantial or indirect and minor, although the term was once reserved for a character's chief opponent. It is also quite possible that a character is his own worst enemy, or is challenged not by another human but by an obstacle, which requires him to overcome not only his own limitations, but the forces of nature, possibly fate, and maybe even society as well. In such cases there is no true antagonist, although one might sometimes be justified in claiming that a character is his own antagonist when the main conflict is man vs. himself, but that's not a given.
In talking and writing about literature, it's important to make sure that your audience has the same understanding of terminology that you do. For example, one might refer to all of the important characters in a story as the "main characters." It would not be wrong to do so, but it could be confusing. They could also be called the chief characters or principal characters or major characters. On the other hand, the term "minor characters" is hardly ever confusing.
Characters are one of the three "unities" of a scene. The other two are time and place. Whenever there is a change in time, place, or characters, there is a change in scene.
Whether or not the narrator of a story is significant as a character depends on the point of view. One might argue that even an anonymous (unknown) third person narrator can be a character, although that depends on many factors, not the least of which is the narrator's relationship to the events of the story. Generally only first person narrators and third person narrators who are minor characters ever figure as characters in the story. Anonymous and omniscient narrators are often personas (masks) for the writer to hide behind; so, while they have tones of voice and attitudes that are uniquely their own, these narrators may be serving the writer the way puppets serve a ventriloquist.