In "Fahrenheit 451" what do the people in hiding at the end of the novel do and why do they do it?
The people in hiding were the ones that Montag ended up with. They greet him and include them in their circle, because they too are outcasts that have been ostracized from their communities. Montag joins up with them, and it isn't much later that the bombs take out the entire city. Everyone and everything in the city is pretty much destroyed, which leaves Montag, Granger, and their clan of outcasts as the only survivors. It is up to them to decide what to do. They could leave, walk away, and find someplace new to live their lives as they want to, or they could stay, go into the city, and help whatever survivors exist there to rebuild. They could try to make a positive impact on the recovery, and try to rebuild things better, using what they have learned about how dysfunctional their society was before.
So, they choose the latter. They choose to go back to the city and to rebuild it the right way. And, they take the wisdom gleaned from all of the books that they have memorized. They each bring their own memorized portion, that will help them to remember how to do things the right way. Granger states of their mission,
"We're going to meet a lot of lonely people in the next week and the next month and the next year. And when they ask us what we're doing, you can say, We're remembering. That's where we'll win out in the long run."
He goes on to say that hopefully they can remember enough to bury all of the past's mistakes and rebuild a better society. So, they head off to the city, and that is where Bradbury chooses to end the book, with you imagining the good that they will do when they reach it. I hope that those thoughts help; good luck!