Minecraft wiki entry for Beginner%27s_guide, associated text: The Pickaxe is used to break and gather stone, metal, and related materials such as ores.
The Axe is used to collect wooden materials more quickly.
TheShovel is used to gather dirt-type blocks: dirt, sand, gravel, clay, and their variations. "Grass blocks" are a variation of dirt.
The Hoe can be used to quickly break some lightweight blocks such as Leaves, but its main use is to turn dirt or grass blocks into farmland.
Special mention for the Sword. Instead of breaking blocks, a sword is used to attack animals or monsters.