When you interact with a Divine fire spirit, it will hop into your inventory so that you can obtain a reward from it, you will obtain bonus experience for the next 1-5 logs burned, and you will earn up to 430 Divination experience. The reward can either be claimed now or at a later time - the Divine fire spirits will not stack in your bank. Note that higher level logs burned and wearing a Fire-based skilling cape will increase the value of your reward. If you are burning Protean logs, it will vary depending upon your Fire spirits and Divine fire spirits for a list of items that can be obtained from each.
Should you wish to use a more afk method, it is possible to strike firelighers. This will enable a buff wherein all Fire spirits that spawn will be automatically placed into your inventory for 5 minutes. Multiple firelighters, of any color, can be struck to make this buff last up to 60 minutes.