This is the 855th most frequent Serbian word.
играчима
The Serbian word "играчима" means "to the players" or "for the players" (dative or instrumental plural of "играч").
In this sentence, 'играчима' is the plural dative case of the noun 'играч', meaning 'players', used to indicate the recipients of the instructions.
Тренер је поделио инструкције играчима пре утакмице.
The coach gave instructions to the players before the game.
'Играцима' is again in the dative case, identifying the recipients of the gift.
Поклонили су поклон играчима који су победили.
They presented a gift to the players who won.
Here, 'играчима' is in the instrumental case, as part of the prepositional phrase indicating 'with the players'.