Cards list various bonuses or penalties you can use to help yourself in combat or on the strategy map, or hinder an opponent. Certain buildings on the strategy map can give you cards every certain number of turns, and you can get them based on your decisions in the RPG phase in the single player campaign. There are mercenary cards that let you bring extra units into battle, cards which give a temporary dragon skill or unit bonus / penalty for one battle, cards that let you build a building on the strategy map for free, cards to increase gold production, block an invasion or prevent certain types of units from moving in a particular country for a turn on the strategy map, etc.
Yes, the full single player campaign will be available at launch (and is currently in the review version that some press has). The original intention was to eventually include the first part of the single player campaign in the public beta.
