Many breakable search objects are scattered in Palaces that can yield certain items. They are generally themed per location, such as how they take the appearance of daruma dolls in Shido's Palace. They can be identified easier via the use of Third Eye, in which case they'll then emit a yellow glow.
The protagonist can interact with them, in which case he'll break them. In the process, he will receive a random item, with the possible options varying between Palaces, or divided between paths in Mementos. In Palaces, destroyed objects will remain as is for the day.
Generally, the items that can be received from these breakable objects are certain consumable items (such as Devil Fruits and Revival Beads), treasure items, which can be sold for a price, and in Mementos only, material items, which are used for crafting infiltration tools. Also, when breaking an object, there is a chance for a Treasure Demon to spawn from it, in which case the protagonist will have to chase it and attack it to initiate battle. Their spawn rate can be raised with the Treasure Trap tool.
In Persona 5 Royal, consumable items can only be found in Mementos, and material items can be found in both Mementos and Palaces. Additionally, in Mementos, certain items can only be found during rainy and snowy weather or weather warnings.