Like much legistation, the role of the letter of marque evolved from it's initial inception to it's eventual demise.
The original purpose of the letter of marque and reprisal (to use the full title), was to allow subjects the ability to gain their own 'recompense' for injuries inflicted on them by foreign powers without the need for the states to go to war. Where "marque" referred to the crossing of frontiers and "reprisal" was the taking of goods in return (for the injuries previously suffered).
...as the delay of making war may sometimes be detrimental to individuals who have suffered by depredations from foreign potentates, our laws have in some respects armed the subject with powers to impel the perogative; by directing the ministers of the crown to issue letters of marque and resprisal upon due demand...These letters are grantable by the law of nations, whenever the subjects of one state are oppressed and injured by those of another; and justice is denied by that state to which the oppressor belongs.
In effect, the purpose of the early laws was to distance the aggresive actions of the subject from that of the state while giving the injured party approval for a measured retaliation.
...here the necessity is obvious of calling in the sovereign power, to determine when reprisals may be made; else every private sufferer would be judge in his own case. In pursuance of which principle, it is with us declared by the statue 4 Hen. V. c. 7. that if any subjects of the realm are oppressed in the time of truce by any foreigners, the king will grant marque in due form, to all that feel themselves grieved.
Again, it's clear that these early laws were intended to apply in times of peace (truce) rather than, as later became the case, in times of war. The process of granting a letter of marque and reprisal also allowed a period for the offending party to make voluntary recompense before a letter of marque and reprisal would be granted.
...the sufferer must first apply to the lord privy-seal; and he shall make out letters of request under the privy-seal; and if, after such request of satisfaction made, the party required do not within convenient time make due satisfaction or restitution to the party grieved, the lord chancellor shall make him out letters of marque under the great seal; and by virtue of these he may attack and seize the property of the aggressor nation, without hazard of being condemned as a robber or pirate. [sic]
My emphasis on the last sentence to highlight that, from the perpective of the injured party, his protection was from being judged a pirate in his own country, i.e. he could return laden with the goods he gained in recompense without fear of being condemned at home. Obviously, these were not international laws, they gave the injured party no protection in the foreign state other than identifying that the party was acting on their own behalf (and not as an agent of their state) to settle a personal dispute.
 Commentaries on the Laws of England, Volume 1, pg 192-3 - Sir William Blackstone, et al.
 Ibid, pg 193
 Ibid, pg 193