Ore is what you get when you mine asteroids. It is then refined into minerals in a station or starbase (POS) and used in the manufacturing process to produce items. Unrefined ore can also be sold, contracted, or used in certain agent missions.
This is an excellent picture that shows where you can find all the different ores in empire space.
Each ore type has two variants of increasing rarity which, when reprocessed, produce an extra 5% or 10% more minerals than the base ore. Ore can also be compressed by industrial processes, producing the compressed version of each type of ore.