A hand is the set of cards that a player receives in a particular round of a card game. It's called a hand because of the simple fact that you literally have to hold the cards in your hand. Here's a picture of a typical hand:
In a standard deck of playing cards, there are four suits: diamonds, clubs, hearts and spades. And the trump suit is a suit that has been chosen to have the highest value in a particular round of the game (or for the duration of the entire game, depending on the game being played). In other words, with cards of the trump suit, you will be able to beat any other card of the non-trump suit. If both cards are trump-suit cards, the one with the higher rank wins.
So, the phrase the trump suit for the hand means that one of the four suits has been designated to rank above all others for that particular round of the game.
Trump suit, by the way, is where we get the expression trump card from. For example:
I have a feeling the prosecution still hasn't played their trump card in this trial—I expect a big revelation during tomorrow's testimony.