Concisely stated, Gresham’s Law claims “Bad money drives good money out of circulation.”
In this scenario, “good” money means a form of currency whose base material is at least as valuable as the face value of the denomination, while “bad” money is an equivalent form of currency whose material value is significantly less than its face value.
Bad money does not necessarily have to be counterfeit, though counterfeit currency (if it cannot be easily distinguished from the real) is a form of bad money. At the time the law was coined, the primary concern separating good money from bad was debasement, the practice of altering or recreating coin money in a way as to reduce its material value (e.g. by shaving off its outer edge, alloying its metal with a less valuable metal, or outright counterfeit of coins from a base metal).
This is, incidentally, why US coins at or above ten cents in value have ridges around the outside. It prevents debasement by shaving around the edge of the coin.
Gresham’s Law is at its core an economic law, since it deals with the decision making process of individuals and paper entities. Assuming that a person might be able to tell the difference between good money and bad, it is in the person’s interest, when making a transaction, to use any bad money before using good. Both monies have the same fiat value for transactions, but good money has an intrinsic value greater than that of bad money. The person holding good money has made a rational decision to keep it in order to maximize the value retained after a transaction. The effect of this is that bad money is nearly always in circulation for transactions while good money is primarily held as stores of wealth.
Countries usually enact laws preventing the conversion of their money into bulk metal (melting it down and reforming it into bars and ingots), but international trade in currency can allow some operators to export money to jurisdictions where this doesn’t apply, profiting off the arbitrage of some foreign government’s money’s face value and its material value, so the strategy isn’t necessarily effective in combating Gresham’s Law when debasing its own currency.
More commonly, governments no longer mint anything but debased money. Because countries have abandoned gold and silver standards for the value of money, in favor of floating fiat currency, it is no longer possible to provide coin money as fixed stores of value. Due to inflation it would soon be worth more than its face value. Instead, relatively cheap metals are used (the modern penny is a thin copper electroplate on a zinc disc, for example) and the legal tender value is maintained by force of law and national stability.
This principle goes back at least as far as Aristophanes, but in 1860 it was named for 16th century financier Sir Thomas Gresham by Henry Dunning Macleod. Gresham’s notable accomplishments include raising the value of the pound sterling to strengthen the ailing financial position of the English royals, and to oversee the construction of the Royal Exchange, a trading floor and center of commerce in London modeled after Antwerp’s stock exchange building. Gresham willed his estate to the City of London Corporation for the purpose of building an institute of higher education (Gresham College), which continues to this day providing free public lectures in ten fields of academic study.