In Pirates of the Caribbean: Dead Man's Chest, Cutler Beckett remarks that he and Jack Sparrow have both left their mark on one another, but a full explanation for what that means is only found in material outside of the films. The Pirates of the Caribbean series follows Captain Jack Sparrow and a rotating motley crew of adventurers as they face threats both historical and supernatural. By virtue of its setting and time period, and as a form of contrast to its lawless leads, the franchise features many characters with some level of connection to the British aristocracy.
Beckett is introduced in Dead Man's Chest as a Director for the East India Trading Company who, in his vengeful quest to eradicate piracy, seeks out the power of the titular Dead Man's Chest. He had made opportunistic use of supernatural forces before, in material outside of the films, namely when forming a brief alliance of convenience with the undead pirate captain Jolly Roger. Beckett in a sense replaces the disgraced Norrington as the primary governmental villain, and in that capacity serves as a counterpart to Davy Jones, who succeeds Barbossa as the primary pirate villain.
When describing his old adversary in Dead Man's Chest, Beckett says of Jack that "we've each left our mark on the other." In the case of Jack, this is a very literal reference to the "P" brand that Beckett had seared onto his skin to mark him as a pirate, whereas Jack's corresponding mark on Beckett is more figurative. As established in prequel novel Pirates of the Caribbean: The Price of Freedom, as a young man, Jack worked for the East India Trading Company after being recruited by Beckett. Although not wantonly rebellious, Jack eventually defied Beckett on principle by refusing to reveal the location of the lost island of Kerma and freeing a shipful of slaves. In retaliation, Beckett branded Jack and scuttled the ship that would become the Black Pearl, but because the consequences of Jack's exploits fell on the head of his immediate superior, Beckett's reputation was tarnished to the point that his social mobility was arrested and his aspirations for a noble title were frustrated. His "mark" was being weighed down by Sparrow's insubordination and his own inability to control him.
The question of social mobility isn't unique to Beckett in the Pirates of the Caribbean films. Most centrally, Elizabeth's love for Will in The Curse of the Black Pearl is complicated by his lower standing, and her ascension to the role of Pirate Lord in At World's End could be seen as evidence of her benefiting from the greater equality offered by the films' grungily idyllic pirate society. However, as is very rarely the case, Beckett had a specific individual that he could blame for his social stagnation, and his vendetta against Jack Sparrow brought a hateful spin to his lifelong fascination with pirates that would have far-reaching consequences.
While the Pirates of the Caribbean series has naturally always turned a skeptical eye toward aristocratic society, the interesting lore addition of a semi-organized Brethren Court meant that a character as mercilessly pragmatic as Beckett (who was even given the dying line of "it's just good business") was needed to reemphasize just how anti-authoritarian pirates were by comparison. But when seen in conjunction with non-film material detailing Beckett's history with Jack Sparrow and his fixation on supernatural forces as a means to an end, he becomes a dispassionate, Machiavellian breed of villain all his own.