Jem is going through adolescence, from child to teenager, and all the concepts of justice, equality and law that he's learned from his father are being challenged by what he sees in the world. He continues to be fair-minded as he has always been guided by his father to stand up for what he believes in; essentially that everyone is created equal. The reason he gets so fired up when Scout brings up the trial is that this is the first dramatic, public event that shows that the world is an unjust, unfair place. So, he's coming to grips with his own development as a young adult, brought up as one who will stick up for the mockingbirds of the world, and he is realizing that parts of the world will be against him. So, he stores parts of this away, until he's a bit older and wiser, allowing him to grow without the burden of explaining an unjust world to Scout.  Essentially, he's trying to be a typical teenager, focusing on football and typical teenage concerns while simultaneously being a young man with Atticus' principles.

This quote occurs in chapter 26. Scout is perplexed about people's self blindness, so she tries to talk to Jem about this. Scout says her teacher, Miss Gates, got red in the face and upset about Hitler persecuting the Jews in Germany. But then, Scout said, she had been at the courthouse and overheard Miss Gates justify persecuting blacks because they were "gettin‘ way above themselves." How, Scout asks, can Miss Gates condemn Hitler for persecuting Jews and then be so "ugly" herself about blacks?

Instead of responding to her question, Jem gets angry, shakes her hard, and tells her never to talk to him about the courthouse again. When Scout goes to Atticus for comfort:

Atticus said that Jem was trying hard to forget something, but what he was really doing was storing it away for a while, until enough time passed. Then he would be able to think about it and sort things out.

What this is means is that Jem is upset right now about the trial and Atticus's participation in it and the way people are condemning him for it. By "storing it away," Atticus means that Jem is storing in the back of his mind everything about the trial that is happening but that he can't deal with right now. It's all too close, too immediate, and too raw for him. He needs to time to process and understand his feelings, and then he will return to normal.

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.