At the beginning of Chapter 22, Jem's "face was streaked with tears" after suffering through the guilty verdict in the Tom Robinson trial. In Jem's mind, Atticus had clearly proven that Tom could not have beaten or raped Mayella, but nevertheless, the jury found him guilty. His realization that a group of white men could rule against a black man in spite of the facts was another example of Jem's loss of innocence.
Jem also reacts angrily when Aunt Alexandra scolds Dill for telling the truth about his Aunt Rachel, who "drinks a pint for breakfast every morning--know she drinks two glasses full. Seen her."
Later, Miss Maudie explains to Jem that Atticus is one of those men "who were born to do our unpleasant jobs for us." She goes on to explain that many white Maycomb citizens actually agree with Atticus and believe that Tom was innocent. Jem responded that "can't any Christian judges an' lawyers make up for heathen juries."
I think that the incident you are probably referring to is the incident with the cake.
In this chapter, Jem and Scout are having to deal with their feelings after Tom Robinson is convicted. They have previously thought that Maycomb was a wonderful place and now they are waking up to the fact that it has its problems. This is part of growing up.
With Jem, I would argue that his growing up is symbolized by the cakes. Miss Maudie has made three cakes -- a big one and two little ones. She cuts from the big one for Jem. To me, that symbolizes that he is moving toward adulthood.