The cards you are holding you are holding are your hand of cards. At the start of each game, both players have 5 cards in their hands. The player who goes first does not draw a card. You may look at them, but don't show them to your opponent.
You still have a hand even if you have no cards in it. For example, if a card tells you to discard your hand and you have no cards in your hand, you can still discard your hand, you just discard 0 cards.
There is no limit to the number of cards you can have in your hand at any given time.