"Dungeons" are places where you fight monsters or bosses.
Alternative names for Dungeons are Quests, locations.
Candy Box 1 Reference:
In the original candy box, after a while, you could unlock the "QUESTS" tab, which gave you access to quests/dungeons.
In Candy Box 2, this may stay the same, or another option could be that the QUEST tab will be open constantly. Maybe there will even be a whole storyline to follow within each dungeon.
Based on the Candy Box 2 screenshot, there is a "Map" button. Maybe from the map you can visit buildings like The Forge and do some quests