The element of fire is used both in purification and for processing ores through smelting.
The main fire blocks are all designed with "popcorn" style smelting capabilities as well as multiple additional options during smelting such as reverse smelting, fuel conservation, accelerated smelting, or even resource duplication. Since these blocks offer the potential to have infinite ingots from a single ore (due to allowed duplication) each block has a chance of failing to smelt the item and fuel costs are very high. The higher tier block, the lower the chance of failure and the higher the chance of duplication.
Active fire elemental magic focuses on offensive power and of course igniting enemies. Buffs allow you to hide from or attract aggressive mobs depending on your current world. The passive ability permanently reduces damage from fire based enemies, fires in general, and lava.
There are various other things available to you if you have the correct mods installed.