The Statue's Bargain
Travel to Hateno Village and look for a small horned statue north of Firly Pond. Talk to it, and it will steal one of your heart containers away! This will trigger the sidequest.
Talk to the horned statue again and it will offer to give you back either your heart container, or 1/5ths of a stamina wheel. Take your pick (obviously, we wanted our heart container back). From now on, you can swap around your hearts and stamina by selling your heart or stamina to the statue for 100 Rupees. Then, pay 120 Rupees for either a heart or stamina vessel in exchange.
This is useful for if you are doing something that will require more life or more stamina than usual, but you do not want to clear more Shrines to get more of either. An example would be if you are hunting for particularly difficult horses to tame and you need more stamina, or if you are going to storm Hyrule Castle and want more life.