Gryffindors are good at one thing, above all others. They have the unique ability to act, regardless of the consequences. This could take the form of standing-up to a bully, even if it means getting beaten up. It could be helping an outcast, even if it means humiliation from the group. The ultimate example is rushing into battle, even if it means getting killed.
The dilemma is, deciding if doing something is worth it, even if you are ineffective? We all want something good to come of our actions. Either we want the bully to change their ways, the outcast to appreciate us, or the battle to be won. Without those things, doing anything loses meaning.
I just saw Wonder Woman, which was absolutely fantastic. 9/10 thumbs up. *Spoiler alert*
Diana suffers from the Gryffindor Dilemma. She knows WW1 is happening and she wants to stop it. She knows that politicians spend all day babbling about finding a compromise. She says, “Cut the BS, let’s just rush into battle and kill the bad guys.” “It’s not that easy, saving the town is a high risk- low reward endeavor.” says her Slytherin boyfriend. Diana, still naive, rushes into battle, wins, and saves the townspeople, thus seemingly proving her boyfriend wrong. Later, the bad guy launches a weapon and kills everyone in the town, which renders her efforts to save said town worthless, proving her boyfriend right. Diana is devastated. A good Gryffindor, of which Diana is a fine example, was only temporarily deterred. The effect was mostly irrelevant. The act of saving the town was important. Whether they live or die, whether they thank her or not, whether they are secretly anti-Semites or not, it shouldn’t matter. The act was important.