To cast a card means to:

Casting a card refers specifically to the act of using a card from your hand to create a spell on the stack. When a card is cast, such as an instant, sorcery, or creature, it is played as a spell, and the appropriate costs associated with that card must be paid at the time of casting. Once a spell is on the stack, it can then be interacted with by players, awaiting resolution.

The other choices do not accurately reflect the concept of casting in Magic: The Gathering. For example, putting a card into play without costs does not involve a casting action—it's simply placing a card onto the battlefield in a way that bypasses the normal casting process. Drawing a card and immediately discarding it again does not relate to casting; it's an action that alters your hand rather than creating a spell. Activating an ability is also distinct from casting, as it does not involve placing a card from your hand onto the stack but instead uses an already-existing effect or ability of a card that is in play. Thus, option C correctly captures the definition of casting a card.