in Hoops by Walter Dean Myers, what do "round" and "flat" mean when referring to the protagonist?
The literary terms "round" and "flat" refer to types of characters in a short story or a novel. Both terms have to do with how much information the author gives us about their characters and what those characters do--or do not do--in the story.
A flat character is a relatively undeveloped character, one about whom we generally do not know much; he is undoubtedly a minor character in the story, though certainly he can be important to the development of the plot. The most important element which distinguishes a flat character from a round character, though, is the fact that he does not undergo a significant change or experience any significant growth over the course of the story.
Flat characters might be thought of as two-dimensional characters or even as stereotypes. For example, if the main character of a novel has classmates, we can expect to find an athlete, a "brainiac," a bully, and a teacher's pet among them. If none of them are really friends with the protagonist, that is probably about all we know about them, though we will certainly see them as they interact with the protagonist. They would be considered flat characters.
A round character, as you have probably guessed, is more of a three-dimensional character, possessing a depth which the minor, flat characters do not possess. In general, we know what a round character thinks and feels as well as what he does. Almost without exception, every protagonist is a round character, because a protagonist is the generally the most significant character to experience growth or undergo change in some form. All of the characteristics which make the protagonist are the same characteristics which make him or her appealing, a person to whom you can relate and with whom you can sympathize.
In Hoops by Walter Dean Myers, the protagonist is seventeen-year-old Lonnie Jackson. We know lots of things about him, including some things he might prefer we did not know if her were sitting in a room next to us (such as the illegal things he does in order to survive). We also know that he has a dream: to become a professional basketball player. He knows what he wants and that he has an exceptional talent for basketball, but he lives in an environment, Harlem, which is not conducive to helping him realize his dream.
One change that Lonnie undergoes is his feelings about his coach, Cal. At times he is furious (for lots of reasons, and once even outraged enough to pull a gun on him), at times he is impressed with him (like when they play basketball one-on-one), and sometimes he even feels sorry for him (like he does after having dinner with Cal and his ex-wife).
His changed feelings toward Cal are one of the ways we know Lonnie has grown and matured over the course of the novel. In the beginning, he sees Cal as a drunkard and immaturely assumes that this is all Cal is or can ever be. Over the course of the novel, Lonnie matures and sees that Cal has value and is even proud of him for overcoming his problems to become a better person.
At the beginning of the novel Lonnie cared about nothing but basketball, but by the end of the story he comes to value people and their struggles, as well as doing the right thing--even when it is dangerous to do so.
Because we know so much about him and because he undergoes this change, Lonnie Jackson is not only the protagonist of this novel, but he is also a round character.