Nuts, Bolts and Thread sizes confuse the feck out of me.

When you see a M8 bolt on the shelf in a shop, what does M8 mean. Is it that it take a 8mm spanner to tighten, it has a 8mm diameter shaft, or is does it mean you drill an 8mm hole before tapping a thread.

for instance

If I need to buy a new bolt and the nut for it takes a 13mm spanner what size is the bolt?

If I want to drill a hole to accept a M8 bolt what size hole do I drill before tapping the thread.