Scout's crying at the end of Chapter 29 comes as an emotional release of all that has happened to her and Jem, including her recognition of Boo Radley and the realization of the magnitude of Boo's heroic deed.
In Chapter 28 after Scout and Jem have been attacked, Scout stumbles toward home, and as she does so, she sees a man carrying her brother toward their house. Later, she tells the sheriff about how she heard footsteps and tried to run, but fell instead and was attacked. After this, she heard Jem cry out and be picked up by a man.
Then, in Chapter 29 when Sheriff Tate asks her who pulled Bob Ewell off of Jem, Scout turns to the man leaning against the wall. It is not until she notices this man's white hands, his hollow cheeks, and his timid smile that she recognizes the recluse of their neighborhood. As his lips part into a shy smile, Scout cries because of her emotional realization that she is looking at Boo Radley in the flesh.
Moreover, she apprehends the courage that shy Boo must have had to summon in order to be able to leave his house and rescue her and Jem. Scout knows that his courageous act was an act inspired by love. All she can say is "Hey, Boo," but it is said with gratitude.
Scout has been remarkably cool and calm as she describes what has happened on her way back from the Halloween pageant. She has finished telling her story to Sheriff Tate, who then asks her who the man was who was "staggerin' around and pantin' and--coughing fit to die." Scout points to the unknown man who has been standing in the corner the whole time.
"... there he is, Mr. Tate. He can tell you his name." (Chapter 29)
But as she, for the first time, takes a good look at the man, Scout notices his "sickly white hands," his white face, his hollow cheeks, and his "colorless" gray eyes. When the man finally smiles at her, Scout suddenly realizes it is Boo Radley,
"... and our neighbor's image blurred with my sudden tears." (Chapter 29)
Scout's greatest fantasy--that of one day meeting Boo and having an innocent conversation with him--has miraculously come true, and the emotion of this revelation causes Scout to run for Jem's bedroom to cover up her embarrassment "by covering Jem up."