A license granted by a government to a private ship allowing it to attack enemy ships. By the 16th century, they were issued as a cheap way of expanding a nation's navy and of bringing in extra income. Letters of marque were very important to pirates, because they gave them an opportunity to operate semi-legitimately -- instead of a pirate, he was now a privateer, raiding for king and country, instead of just for his own treasure chest. If he was captured, he couldn't be executed, since he was operating with the approval of his home nation.
However, letters of marque didn't always save a privateer from execution -- Spain, for example, never recognized any nation's letters of marque, and the evidence that Captain Kidd carried letters of marque was suppressed for political reasons...
Research: GURPS Swashbucklers, Third Edition, by Steffan O'Sullivan, (C) 1999 by Steve Jackson Games, p. 59.