Characterization (Brit. characterisation) is how a character is described: the traits, actions, manner of speaking, etc., that make them them.
When borrowing other people's characters, as in fan fiction, it isn't enough to just weld a name onto an amorphous humanoid thing and make it do what you like; if it doesn't speak like the character, act like the character, or do the things the character would do, then it probably isn't the character. When this happens, the real character has been sucked into a plothole, and their place usurped by a character replacement. Agents must in these cases kill the replacement and find the real character.
When writing an original character, it is equally important to stick to one's own characterization and to not tack on character traits for no reason. For instance, if the character has a tragic past, that should have a reasonable effect on the character's thought and actions in the present, whether they've come to grips with those events or not. It should not be an excuse for wangst or a once-off bid for the readers' or other characters' sympathy, mentioned once and never playing a role in the story again.
Similarly, description does not equate to characterization. Being the most beautiful girl in the world doesn't mean other people will instantly like her if she acts like a spoiled brat; that goes double for having color-changing eyes or an unusual name. It is the character's speech and actions that defines who they are more than any physical traits.
Of course, a physical trait can be used in characterization, if that trait has some plausible effect on how the character behaves and how others react to them. Harry Potter's scar is a good example of this: a scar in and of itself is meaningless—everyone gets a few scars in the course of a lifetime, especially cat owners—but in this case it is a visible reminder of everything that has happened to Harry, and other people instantly recognize it when they see it. How Harry deals with that is an important part of his character.