Blue logs are created by using a blue firelighter (obtainable from completing any clue scroll) on some normal logs. The raw materials for this process cost 297 coins.
When these logs are burned, they create a blue fire. This action awards 50 Firemaking experience, 10 more experience than lighting regular logs. When blue logs are added to any bonfire, the colour of the flame will change blue.
Blue logs can be added to the Odd Old Man's pot boiler, but the resulting fire will be normal, and your logs will be lost, so this is not recommended.