Why does Tris and Tobias want to go "outside the fence"?

There are quite a few questions here. I will answer your first one:

After Edith Prior's video footage reveals to the city that there is a whole world outside of the city limits, the city's social system is in shambles. The factions have disintegrated, and Evelyn rules the city as a tyrant with her factionless army. Tris, Tobias, and their friends set out on a mission to discover what is outside the city.