Pickaxe power

Pickaxe power is the amount of strength your Pickaxe or drill has. It determines how much you will damage a block before it breaks. Some blocks break instantly, other blocks cannot be mined with low Pickaxe power. Pickaxe power has no effect on Mining speed in terms of Use time, but lower Pickaxe power will generally create the illusion the Pickaxe is slower.

Source
Every tile has 0 hit points to start. Once a tile's "hit points" hit 100, the tile is destroyed. A tile's hit points are increased every time it is hit with a pickaxe. Certain tiles will reduce the amount of damage done to them. These tiles include:

This determines how many picks it takes to destroy a block. After determining the damage done to a block, Terraria will then determine if you should be breaking the block instantly, or not at all.


 * Here are all the instances where Terraria stops the destruction of a tile-


 * And here are the instances where Terraria will kill the tile instantaneously.