The circus screen is the hub world where you'll end up after each mission. From here you're able to access every available building in your circus to develop your crew, assign characters to specific tasks unlocking boni or resources for the next mission.
Each time your circus levels up you're able to upgrade every building available to you, for a price.
The train station is where you unlock new characters to add to your roster. Every time a new character class is unlocked, it becomes available for hire here. Apart from special story characters, this is the best way to actually chose the performers you add to your team by looking at either of their ability sets (see classes), circus compatibility and circus roles. (see circus performance)
The sleeping cart is a building used to regenerate characters during your next expedition. He is unable to participate in any other activities for the next expedition but will get HP back, with a sligh increase in devotion too in exchange of meat.
The circus tent is a building used to increase XP of characters that would otherwise just stay idle during the next expedition.