What does "proof" mean on alcohol?

Those are two very interesting questions, actually, and both have fairly obscure answers. The short answer to the "proof" of alcoholic drinks, however, is that it is double the percentage of alcohol in the beverage.

For example, a "six proof" beer would have 3% alcohol, barely any, while a strong liqueur that advertised it was 80 proof would have 40% alcohol.

It isn't, however, quite that simple...

The measure of the percentage of alcohol in drinks is widely believed to have started in the 18th century, when alcohol and gunpowder would be mixed together: if the combination lit when a flame was applied, it would be considered to have "proved" it was a strong alcohol. Originally that was considered 100 proof (e.g. "100% proof") and was actually 50% alcohol, but more sophisticated measures since then have established that this alcohol and gunpowder mix would ignite if there was at least 57% alcohol, not 50%, so it's not quite the 2:1 measure we're used to.

As an interesting aside, the phrase firewater is believed to have come from this test for alcoholic content: if the liquid did catch fire you can only imagine the impression it would make on the locals in the saloon!

Wikipedia has an interesting entry on this issue, including discussion of the original hydrometer used for more formally measuring alcohol content, the Sikes hydrometer, invented by Bartholomew Sikes, of the London Excise Commission, back in 1802. Why did the government care about percentage of alcohol? Because excise tax was charged based on how strong the liquor, so being able to accurately measure alcoholic content was good for the government coffers.

Finally, a standard "drink" of alcohol is considered to be 1.5 oz of 80-proof alcohol. Not very much, less than an ounce of pure alcohol.

In terms of gold, just remember that 24K gold is 100% pure gold. That means that you can always calculate the percentage of actual gold in an alloy (e.g., mix of metals) by dividing by 24 and multiplying by 100. Do that for 18 karat gold and you'll find that 18K gold is 75% gold, 25% other metals (18/24*100 = 75). When you get down to 10K gold or lower, you're really buying a lot of other metals with just a small percentage of pure gold too (10K = 42% gold, 58% other metals).

One of the most common metals to mix with gold for jewelry and industrial use is copper, interestingly enough, a metal that has market value of its own accord. Most gold coins in circulation, even back in the days of the Spanish Main, were 22K, so if you happen to have a chest of doubloons in your closet, it's not quite 100% gold after all.

Hope those answer your questions!