What a jersey card is
A jersey card is a trading card with a small window cut into it, and behind that window a piece of fabric — a swatch of a jersey associated with the player on the card. You can touch the actual material.
The broader category is called relic cards or memorabilia cards, and it covers more than jerseys: patches, bats, gloves, balls, and other pieces of equipment have all been embedded in cards.
Game-used vs. player-worn
The detail collectors care about is provenance. A game-used relic comes from a jersey the player actually wore in a game. Some relics are player-worn (used in an event or photo shoot) or simply "event-worn," which carries less weight.
Card backs usually state the provenance in fine print. "This jersey was worn by the player in an official game" is the one collectors prize.
Why they are thicker and pricier
Embedding fabric makes relic cards much thicker than a standard card — often 35 points or more, compared to the usual 20 to 24. They need oversized sleeves and holders as a result.
They are also a premium product: relics are inserted as chase cards in packs and command higher prices than base cards, because you are getting a small piece of the real thing.
Relics and custom cards
Custom cards do not contain fabric — they are printed keepsakes, not memorabilia cards. But they borrow the same appeal: a card that is personal and tangible. A custom card of your kid is, in a sense, the ultimate relic — the only one of its kind, about the player who matters most to you.