There are multiple locations you can choose to send Avery to explore, each with their own unique rewards. Some areas drop food, some areas drop resources, and others drop furniture!
While exploring you should be able to see information about the currently active expedition, Lap Meter as well as the Stats menu which will show your stats related to the current expedition.
Avery can typically explore without needing to equip a specific skin, though some locations require one, such as: Underwater Ravine and Moon.