Here, price means inflation or deflation. So this funny term really means a "mechanism linking inflation/deflation with gold flows.".
Through this mechanism, it was thought that the gold standard had a wonderful built-in adjustment mechanism. Even if governments did nothing, international macroeconomic adjustment would occur automatically, or so it was argued. It works like this:.
If a country has a current account deficit for any reason, there will be an outflow of gold. The loss of gold means less money supply, so this country will have a price deflation. After some time, its products become cheaper in the global market, so exports will rise and imports will fall. This improves the current account.
It works just the opposite for a country with an initial current account surplus. It will accumulate gold, which increases money supply and raises the price level. The country loses price competitiveness, so the trade balance worsens.
The price–specie flow mechanism is a logical argument by David Hume (1711–1776) against the Mercantilist idea that a nation should strive for a positive balance of trade, or net exports. The argument considers the effects of international transactions in a gold standard, a system in which gold is the official means of international payments and each nation's currency is in the form of gold itself or of paper currency fully convertible into gold. Hume argued that when a country with a gold standard had a positive balance of trade, gold would flow into the country in the amount that the value of exports exceeds the value of imports. Conversely, when such a country had a negative balance of trade, gold would flow out of the country in the amount that the value of imports exceeds the value of exports. Consequently, in the absence of any offsetting actions by the central bank on the quantity of money in circulation (called sterilization), the money supply would rise in a country with a positive balance of trade and fall in a country with a negative balance of trade.