One reason that Jem is crying is because Nathan Radley lied to him about the tree being sick; Jem asked Atticus if it looked sick and he said it didn't, so this disappointment in a person's lies could be one cause of Jem's tears. More likely though, Jem is upset because their connection to Boo has been lost. They were just starting to form a bond, and Jem is realizing that Boo is lonely and reaching out for friendship. When that is taken away from him, it upsets Jem to the point where he starts crying.
