Sometimes you can see the message "Dinner table full" when trying to get a cooked dish from the hearth or from the cooking table. It means that all the available slots on the dinner table are already taken by other dishes. The only way to empty your dinner table is to feed any dish that is already on the table to the family.
To feed the characters you will need to open the dinner table, drag some available meals into a free slot, and then tap the "Eat" button (the plate icon on the right).
Note: if you see the message "Everyone is full" when you try to feed the family, that means you have too much energy, so the family can't eat. If this happens, you need to spend some energy before feeding them. If you want to collect a lot of energy, feed the family first and collect the energy from the chests/merchant/shaman/gifts/energy packages afterwards.