When you interact with a Fire spirit, it will hop into your inventory so that you can obtain a reward from it and you will obtain bonus experience for the next 1-5 logs burned. The reward can either be claimed now or at a later time - the 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.
Note that enabling the "Fairy fire" perk at the Memorial to Guthix will cause a Divine fire spirit to appear instead. This spirit offers different rewards and will award you with up to 430 Divination experience.