It is always somewhat dangerous to set up ready-made categories and then apply them to something as various as a work of art, but certain definitions can help us to a clearer understanding of the characters we meet in Adam Bede.
A flat character is a one-sided figure, a character who exhibits only one or two human traits, usually in exaggerated form. Such a character's speeches and actions are never very surprising because they always spring from the same motivations and preoccupations, and he normally does not change at all in the course of the book. An example in Adam Bede is Mr. Casson, the innkeeper. Mr. Casson is very much impressed with his own importance, and whenever he appears in the novel, he is asserting or defending his dignity. He is a man with an inflated sense of his own importance, and that is all he is. In the same way, Mr. Craig, the gardener at the Chase and another of Hetty's admirers, is a know-it-all, and whenever we meet him he is dispensing (often false) information. Real people are never as simple as figures like these. The characterizations are superficial, static, "flat."
Round characters, on the contrary, possess the complexity which is the norm in real life. They are flexible and change in response to changed circumstances. Adam, for example, is capable of being harsh, gentle, loving, cruel, violent, shy, and so on; he has not one trait but many. And he learns a great deal in the course of the novel and changes gradually from a rather brash and immature youth to a self-disciplined and emotionally stable man. Adam is a "round" character, a fully developed and plausibly human figure.
A central character is one who plays a major part in the story and has a hand in the shaping of events. Central characters do meaningful things and have meaningful things done to them. A background character is normally not "on stage" very much, at least in comparison with the central characters. He can serve many purposes: he can help create atmosphere, as Wiry Ben and the other townspeople do; he can provide comic relief, as the men at the harvest supper do; he can provide incident, as Molly does when she drops the ale jug. But straight background characters do not affect the plot line in any very significant way; the drama moves around them, but it never really touches them.
