From Lunia Wiki

Secret Areas are small, hidden areas within a stage that, when found, give you a small amount of exp. They usually have a chest (Suspicious Box) and an enviormental healing item (such as a Coconut Tree or Aloe). The chest can be attacked. Doing this will normally open the box and drops items; one for each member of the party. Sometimes, however, the chest will attack back. When this happens, you must defeat the chest for your items; it'll only drop one, no matter the number of players in your party.

It is generally looked down upon to go straight for a secret, leaving the rest of the party to deal with any monsters.