bowl, cup, small tray
瓯 centers on a small open container: a bowl, cup, or small tray used for holding or serving things.
瓯 is the simplified form of 甌. It combines 瓦 (earthenware) with 区, which likely contributes the sound, to express a small earthenware vessel.
The left side 区 looks like a divided area, and the right side 瓦 means earthenware. Picture a small clay bowl or cup that holds a partitioned serving of food.
For オウ, imagine an owl-shaped bowl: owl -> オウ, and the bowl is made of earthenware.