The item baskets are the Daily Quest task prizes. You can win them by completing the Daily Quest tasks.
Once you have a required item on your board to complete a task, you will see a purple checkmark near the item. Please open your game's main page and click on the purple chest icon at the top-left corner to see and complete the Daily Quest tasks.
Press the 'Collect' button on a task to complete it and claim its reward. The required item will be removed from your board, and the prize basket will be added to your item queue under your game board.
Put your baskets on your board and tap on them to spawn items. The basket will destroy itself after emptying it.