Forbidden cards are essentially "banned" cards, while limited simply means that you can only put 1 in a deck, semi-limited is up to two in your deck only. Some cards in the OCG/TCG are either forbidden, or limited, and this is due to their ability to create an unbalanced experience for the game.
Unlike in the TCG/OCG where you can have multiple limited cards with different names in your deck, in Duel Links you can only have a total of 1 limited card in your deck. For example you have limited card A and limited card B, and you already put 1 card A in your deck, you cannot add card B to your deck even if they are not cards of the same name. This rule is also true for semi-limited cards in which you can only have a total of 2 semi-limited cards in your deck.
for those of you who may be confused about the inclusion of enemy controller keep in mind this is one of the most popular meta cards and since you can only have up to two semi-limited cards in total this could disturb quite a few meta decks