Base Camp is your base of operations on Tumblecube Island. You can cook there, and decorate your camp.
While in your base camp, tap the cookpot to open the cooking interface. You can add ingredients that you have found during expeditions. Tap the Auto-Set button to automatically insert random ingredients. The ingredients that you put in will determine which meal is cooked. After discovering a meal, the recipe will be added to your list for future reference. Some recipes are secret, and you will have to find the combination yourself.
Meals will be complete after you have completed the required number of expeditions. Return to base camp after that, and the meal will be complete. New pokémon may appear when a new meal is complete. Certain pokémon may be more likely to appear depending on which meal you made. Sometimes pokémon that you encountered during an expedition will show up, as well.
You can use PM Tickets in the Poké Mart to buy decorations for your Base Camp. These decorations have various beneficial effects.