Why does Jem have to forget "something," and how is "storing it away" part of growing up?
Lee's "To Kill a Mockingbird" is at its heart a maturational novel. (You may have also heard the literary term for this, bildungsroman). As such, there are a great number of things Jem must forget in order to reach a new level of maturity.
One of the things he must forget is the way Atticus had to shoot the rabid dog. He is stunned by his father's skill, but must process the event and understand that just because you are good at something doesn't mean you have to necessarily use that skill. (Fighting is another example; one may excel at fist fights, but it's not a good idea to resort to them often.)
Jem must also forget how he has treated Boo, the way his father was treated for seeking equality and justice, and above all, the way Tom was treated with prejudice and malice.
But an important distinction here is forgetting the acts of injustice and cruelty, not the lessons learned. Those lessons must be "stored up."
From all of these events, Jem learns to treat people on a much deeper, kinder, and more understanding level. He has matured a great deal by the resolution of the novel...coming a long, long way from the boy who "dared" to touch the Radley home...a long, long way from the boy who thought justice would always prevail.