Cost (コスト Kosuto) is what is needed in order to play a card.
The Cost of a card is located in the upper left corner of the card, just below the Card Type. To pay the Cost of a card, Sleep a number of cards in your Resource, equal to the Cost of that card. Also, you must Sleep at least one card with the same color as that card. For example, in order to play "Queen of Desert, Cleopatra", a Cost 3 Red Z/X, you have to Sleep at least one Red card and two other cards of any color in your Resource. Colorless Cost can be paid with cards from any color.
Several cards is able to reduce the Cost of a card (e.g. "Country-Eating Manticore"). However, almost all of them also comes with "the Cost cannot be equal to or less than 0" clause, preventing the player to play the card without paying the Cost. Some cards (e.g. "Four Archangels - Michael S.K.") may instead possesses an ability that allow the player to play a card without paying the Cost.
Cost of Ability
Startup Ability also has its own costs, which are shown as <○○> or ○○ ( <Cost> ○○ ) in the card text and must be paid in order to use the ability. Other than Resource cost, the costs of an ability may also require you to (Sleep) the card or to do some other action. If the ability listed more than one costs, all of them must be paid.