Every time I mine I either find redstone, coal or iron. I understand coal and iron but what is the purpose of redstone?
Redstone is used for several items such as compasses (surround a redstone with iron) and watches (surround a redstone with gold) and an ingredient in extending the length in potions.
More importantly, it is used to make redstone wire when placed on the ground. This can transfer the energy produced by, for example, a lever to a door several metres away. This is only the simplest use for it- more complex uses include traps, automatic reed farms, locks and even a simple calculator.
For more information, check the wiki: http://minecraft.gamepedia.com/Redstone