The profit made by a government from the printing of money, literally the face value of the money minus the cost of physically making it. 
Seigniorage is the revenue governments derive because the cost of minting coins or printing paper money is less than the market value of the money. 
The basic idea of seigniorage is that whenever the cost of producing the money used in circulation is more than the intrinsic value of the money the government loses money on seigniorage, while if the market value is higher than the cost of producing the money the government makes money on seigniorage.
Essentially, it is the value the government generates by adding its stamp to an ordinary piece of paper, piece of metal or nowadays an electronic bank entry.
Paper/ electronic fiat money generally has high seigniorage because you do not have to source physical metal to create it, while coins have lower seigniorage because it costs something to create the coins and source the metal. 
Today, seigniorage is associated with central banks and issuance of notes.
In 1290, King Philip IV of France did not have enough money to pay for his wars, so he began to debase the currency by increasing the seigniorage he extracted from melting new coins.
This policy produced a devaluation of the French currency, inflation and the disappearance of gold and silver from the kingdom.
This is exactly the same as printing money, an increased monetary base with less intrinsic value creates inflation, as defined by Irving Fisher’s theory. As the level of goods available for sale are exactly the same, more money in circulation results in higher inflation as these goods will be sold at higher prices to compensate.
To secure cash the King had to arrest the Lombards (1292), then the Jews (1306) and finally the Templar Knights (1307), and confiscated their assets to issue new coins.