Jack gets a novelty item or another worthless gag gift, like a pair of Groucho glasses or a whoopee cushion, from a stranger. For the rest of his life, he considers it his most prized possession just because it was given to him.
Downplayed: Jack owns seven swords, and the one that was a gift is slightly more important to him.
The sword is magically bound to Jack.
The item is a marker of some special relationship (like a wedding ring).
Zig Zagged: The sword was actually cursed, and the Reasonable Authority Figure knew it. Except that it has good powers too, and he can manage with the curse. The sword is no better than any other sword he could have gotten from a swordsmith...but the knowledge the king gave it to him means that he gets more support from the people. But it can be tracked, and hoofbeats come along to find them while deep in enemy territory, oh no! Wait! The Cavalry has arrrived!
No one considers gifts to be particularly important.
All objects are bought or won.
Enforced: "We've got a merchandise deal to produce those emerald swords, so Jack needs to keep his at all times."
"No, Jack, you want to keep that sword; these are just random swords, and that's a gift"
"Why does he keep that thing around?" "You're asking me? Probably because it was a gift or something."
Conversed: "Why does Jack use a sword when everyone else has got pistols?" "It was a gift."
Deconstructed: The villains take advantage of Jack's gullibility by going into disguise and gifting him an utterly useless weapon. Naturally he can't resist using it, and is quickly whipped by foes with superior weapons.
Reconstructed: ...Except that he isn't. He wanted to make the giver happy, so he spent so much time training with the "useless weapon" that he ends up using it quite effectively.