Ores are mined from the world and smelted into bars at a Furnace to craft tools, weapons and armor. Each tier — from copper up to Luminite — needs the previous tier's pickaxe power to mine.
Pre-Hardmode: Copper/Tin, Iron/Lead, Silver/Tungsten, Gold/Platinum, then Demonite/Crimtane and Hellstone. Hardmode adds Cobalt/Palladium, Mythril/Orichalcum, Adamantite/Titanium, then Chlorophyte and Luminite.
Each ore needs a pickaxe (or drill) with enough pickaxe power. Smelt the current tier into a better pickaxe to reach the next, and beat the Mechanical Bosses to unlock the Hardmode tiers.