Mintage number refers to the number of coins struck (manufactured if you like) for that year - so you can see some coins are produced in vast quantities, others in far less. But don't think this means a large intage figure means a common coin. Some countries melt down old coins, so the UK decimal half penny for example is far less common than you might think (but still common).
Proofs are special high quality versions of a coin, often produced on a separate machine, specially polished etc, and then supplied encapsulated in plastic.
