Iron pyrite is a mineral that bears a resemblance to gold, but in terms of value, it does not compare; hence its been given the nickname "fool's gold."
This phrase comes from the fact that there is a mineral that looks similar to gold in appearance, and as a result, it fools many people. As an example, look at what happened to an English seaman by the name of Martin Frobisher. During the second half of the 16th century, he made three trips to Canada. On his second trip he found a mineral that he thought was gold and so he carried hundreds of tons of the stuff back home with him on three ships, where he made a fine profit. 

Intrigued, Frobisher returned to Canada with several additional ships than he had before in order to mine and carry even more of this "gold" back with him, and that's exactly what he did. After years of smelting, eventually it was figured out that this wasn't gold at all, it was actually just a worthless (in terms of value) mineral known as iron pyrite.

The phrase makes an early appearance in 1872, where an article entitled "Fool's Gold and How we may Know it," is found in the Indiana Progress newspaper. There it reads: 

    "There are several minerals which are sometimes mistaken for gold, but the two which are most apt to 
     give rise to deception in this matter are pyrites and mica, and hence they are sometimes called fool's gold."
Common Phrase Origins and Meanings  |  F-Letter Sayings
Note: The origins for many popular sayings are not clear. Thus, in cases like these, I'll either list a theory or two that speak about how an idiom may have originated, or if not that, then I'll try to find the earliest known quote of the phrase being used in writing to give an idea on how old it is. So, for example, if the earliest citation that I can find of a phrase is from a newspaper in 1750, then it is at least that old. Obviously, though, since the expression was already being used in a newspaper, then it is probably already an established saying at that time and is thus older.
* I was short on money, so, after discussing it with my wife, I bought her some jewelry made out of fool's gold rather than the real thing
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A list of phrases starting with the letter - F.
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