A flat character is simple and two-dimensional. His or her personality can be summed up in a sentence. For instance, in Jane Eyre, the hypocritical Brocklehurst and the vapid Blanche Ingram are flat characters. Round characters are the opposite. They seem to have an interior life. One can imagine having a conversation with them in which they might say something surprising or change their minds. Jane Eyre herself and Edward Rochester are both round characters. Unsurprisingly, it is usual for protagonists and major characters to be round and for minor characters to be flat.
The categories of static and dynamic character often overlap with those of flat and round but they are not the same. A static character stays the same throughout the text. A dynamic character changes and develops. In general, flat characters are more likely to be static and round characters to be dynamic. This is generally the case in Jane Eyre, where Jane and Rochester are both dynamic and the more minor flat characters are static. However, St. John Rivers is an example of a character who has some intellectual and emotional complexity and is therefore somewhat round (since clearly there is a continuum of roundness) but does not change at all, despite going to the other side of the world. He is not, therefore, dynamic.