Firestone is a material that can only be found in the Nether. It can be used for a lot of things, and is really common.
Firestone ore is the ore that produces Firestone. It is commonly found in the Nether. It is mined like any other ore.
It looks like netherrack, mixed with orange streaks. Firestone looks like an orange lapis lazuli piece and you get about the same amount of firestone from firestone ore as you do with lapis from a lapis ore.
You found it? You have luck man...
Firestone is the material that is produced when the ore is mined. It can be made into firestone armor and firestone weapons. Firestone axes will also get normal logs from icy logs found in Taiga biomes. When the weapons and tools are used on the overworld, the material it was used on will catch on fire. This is very useful for killing mobs.
One unique property of firestone pickaxes is that they will cook whatever you mine with them. For instance, if you mine gold, iron, or platinum with a firestone pickaxe, you will get the ingot instead of the ore. Sort of like a portable furnace. also, with stone instead of getting cobblestone you get stone, since it gets cooked. For other blocks like diamond ore, nothing special will happen and you will get the standard ore. However, when "smelting" an ore, like gold ore into gold ingot, it takes slightly longer to mine, although it saves time in the long run since you do not have to cook the ore in a furnace