Combine a few drops of liquid dish soap and 1 cup of water in a small bowl. Mix thoroughly and agitate the water to make lots of suds. Dip a sponge into the suds and use this solution to clean all of the leather on the headboard. Wipe it dry with a towel.
Adjust your iron to the cotton setting. Place an old cotton T-shirt over the indentations on the leather and hold the iron over the damaged area for a few seconds. The heat from the iron will remove the indentations while the fabric of the T-shirt protects the leather.
Apply a leather conditioner to the headboard. This will restore the original sheen to the leather and help to protect the headboard from dents in the future.