Burnt jogre bones are made by using jogre bones with a furnace or a tinderbox. They are used in the Tai Bwo Wannai Trio quest.
A common misunderstanding is that they can be burned by using them on the fire. Rather than becoming burnt however, you will receive the message "You heat the bones over the fire, but they don't look any different." If you use burnt jogre bones on a fire you will receive the same message. It is interesting to note that although there seems to be no point in using jogre bones or burnt jogre bones on a fire, if you have multiple bones in your inventory the normal cooking window will still appear asking you how many you would like to cook. It may be that in the past these bones could have been created via a fire, as a previous version of this page stated "If they are burned this way (by using a fire) they will be rejected by the brother in the quest."
When making burnt jogre bones, if a player selects the "light" option when right-clicking on jogre bones without level 30 Firemaking the player will receive the message "You need a firemaking level of 30 to burn Jogre bones. You could find some other way of burning them." hinting that you need to use a furnace to make burnt jogre bones.