When a player transfers to another club, the cards that start coming in packs have got the new club on it. That's what is called transferred card. The cards that already existed remain the same, with the old club on it.
Each year there are two transfer seasons throughout the game: winter and summer transfers. The first one happens in January / February and it implies on there being two cards of the same player. The summer transfers update is there for the transition between games and corresponds to the start of the season for major European leagues. Until the next FIFA launch date, a player may have two cards with two different clubs but only the new one will be released in packs. The Transfers are released into FIFA Ultimate Team Packs periodically in batches, as they take place.
Once the new cards are released, league/club possible combinations increase, which makes it easier to build squads with good chemistry.