Holling Hoodhood wins his race in the cross country meet the exact same way that most great runners win. Holling is blessed with a mixture of natural talent, hard work and determination, and good coaching. Mrs. Baker is a former Olympic medalist for running, and she takes Holling under her wing and helps him with tips on form and training. As a very young athlete, Holling is able to make the varsity squad. All the coaching in the world wouldn't have let him do that if he didn't have the natural ability and dedication to train in the first place. Holling also has the added benefit of encouraging friends. Regarding the meet in question, Holling knows that several other athletes are gunning for him and want to somehow ruin his race. Knowing that those saboteurs are there allowed Holling to be prepared to respond. He responds and wins.
The win is significant because it further reinforces Holling's positive attitudes about himself. His home life is not good, so about the only good things in Holling's life at this point are his small friend circle, Mrs. Baker, and running. The win allows Holling to feel accomplished, it helps him further respect Mrs. Baker and her vast knowledge reserves, and it allows him and his friends to grow closer.