Durability is applied to Pickaxes and appears beneath the item as you show in your screenshot. As you mine, the durability of the pickaxe decreases. The pickaxe works until its durability runs out (when there is no longer any red in the bar). Once durability runs out the axe becomes very ineffective, but does not break and remains in your inventory for use.
Crafting a new pickaxe out of your used one repairs the pickaxe completely (a pickaxe has no lost durability if the bar does not appear beneath the icon). You can also repair a pickaxe with ores you mine. To do this, select a stack of ore and then right-click on the pickaxe (you do not need any sort of crafting table or anvil). Different level ores repair different amounts of durability and higher level axes take more repair.
In Short: Durability is a trait for pickaxes that decreases as you use
the pickaxe. When durability runs out the item stays in your
inventory but becomes extremely inefficient at mining. You can repair
a pickaxe using ore.
Note: According to a post by the game developer, the plan is to have returning to your ship auotmatically repair your pickaxe, but this has not yet been implemented.
You can read the various Starbound Wikis' articles on durability here: