Level refers to three separate concepts.
Profile Level is displayed on your profile and determines what is available in the Shop. It is increased by gaining experience in Multiplayer. Experience is gained whether one wins or loses. One cannot go down in level.
Character Level is a character's current amount of progression through the Normas. It represents progress towards victory, and allows one to meet the level requirements of cards. Character level does not increase a character's stats.
Card Level represents the required character level neccessary to use a card. Generally, cards with higher level requirements have more powerful effects.