The Pickaxe of the Core is one of Thaumcraft's "elemental tools", offering short-range ore detection, and ore multiplication by way of "native clusters".
When right-clicked against a block side, glowing lights will show the location of any ores, water, and lava within 8 blocks. (A number of "false markers" will flash for a fraction of a second, while the true markers will take a few seconds to fade.) While all ores show as identical lights, some ore veins can be partly identified by their arrangement: Coal has much larger veins, and infused stone (shard ore) is arranged differently from vanilla ores. Isolated lights are likely amber ore or cinnabar (amber is more likely near the surface, while cinnabar is common at deeper levels). This ability is very powerful when looking for the more valuable ores, especially when diamond hunting!
When mining iron, gold, or cinnabar, this pickaxe can return a "native cluster" instead of an ore block. The native cluster will smelt into two ingots (or drops) of metal instead of the usual one. The Fortune enchantment will sharply increase the chances of getting a native cluster, up to 25% per level. The user can also repeatedly place and mine any ore blocks that were mined, until all the ore is converted to native clusters. Silk Touch will not prevent conversion into native clusters.
As a bonus, if the pickaxe is used to attack a mob, it will set them on fire.
In older versions, the pickaxe would "detect" a number of other blocks, including wood, sandstone, crafted blocks, and mod blocks.