Stuffed whale is a date gift similar to the Stuffed Penguin and the Stuffed Bear. The three can be used to convert all broken heart tokens into something else.
The Whale converts them into Sentiment tokens, which makes it easier play other date gifts with extra Sentiment. Since late game dates have quite a few broken hearts at the start, this should be used as soon as possible to generate sentiment points for other item combos.
The fourth item that can remove all Broken Hearts from the grid is the Stuffed Cat. It only removes the tokens and doesn't grant any benefits.