What is a round character?
There are four basic types of characters found within a text: round, flat, static, and dynamic. Round and flat characters exist as opposites, as do static and dynamic characters.
A round character is one which is defined completely by the author. A round character is described using both direct and indirect characterizations (direct is where the author tells readers exactly what/who the character is; indirect characterizations are where the reader must infer as to who the character is through their actions, thoughts, and dialogue).
Flat characters, in contrast, are the characters which the reader does not know much about (given the lack of characteristics defined by the author directly or indirectly). These characters typically tend to exist in the background of the story and fail to have much true impact on the other characters.
A dynamic character undergoes dramatic change over the course of the text. What this means is that they tend to make changes (or the changes happen) which alter their way of thinking, acting and /or behaving.
Static characters, on the other hand, fail to change at all over the course of the text. Their mentality, behavior and thinking stay as they are described from the beginning through the end.
Typically, a round character tends to be dynamic--given their character is so completely described that changes made are readily apparent to the reader.
A flat character is a character that is one dimensional and can be readily described in terms of one or two salient characteristics. Think of the typical villains and heroes in action films -- they are either good or bad. You can describe them in a single sentence. In a sense, flat characters are stereotypes, such as "the hooker with a heart of gold", "the wise-cracking sidekick", "the blonde bimbo", "the creative rebel who always knows best", etc. A well-rounded character, like most real people, is complex, a mixture of good and bad, who may be nice to some people and rude to others, sometimes cheerful and sometimes unhappy, sometimes makes good decisions and sometimes makes bad ones, and who develops over the course of a book rather than remaining static.
In general, novels of plot (action stories, adventures, etc.) have flat characters, as do oral traditional epics, and psychological novels tend to have multi-dimensional characters. Although some critics look down on flat characterization, it is technical necessary to maintain the pacing in certain types of novels of plot, such as mystery and adventure stories.