Material Level 1. Wood can be collected with your hand and is required with almost every crafting recipe in the game. Wood is found almost everywhere. There are no wood combat tools.
Material Level 2. Stone can be collected with a Wood Pickaxe and many crafting recipes require it. Stone is also found almost everywhere, but it isn't as wildly common as Wood.
Material Level 3. Gold can be collected with a Stone Pickaxe. This is an uncommon resource, and you will likely have to look for it.
Material Level 4. Diamond can be collected with a Gold Pickaxe. You will likely have to go to a place where Diamonds are more likely to spawn such as the southeast island, the northeast peninsula, or the center to find it as it is otherwise very rare.
No Material Level, and is obtained by killing a wolf or bear. Used to make armour and the Slingshot.