A Monster's attack power determines how much damage it deals when it lands an attack.
Attacks come in three different forms: Melee, Ranged, and Magic. A card’s attack can vary based on the card itself as well as the level of the card and can be affected by the abilities such as Inspire and Demoralize abilities. A unit's attack determines how much damage it can deal when it attacks an enemy monster in battle.
Every melee attack unit has a certain amount of melee attack points with which it enters each battle, this is indicated by a circular blade icon on the card. Melee attacks are normally only for close range (unit in the 1st position). There are several exceptions to this rule, such as the Sneak, Opportunity, and Reach abilities.
Some units have ranged attack, which is indicated by an arrow/target icon. Range attackers can attack from any position except the first position unless the Close Range ability or the Close Range ruleset is in effect.
Other units have magic attack which is indicated by a purple cloud with a lightning icon. Magic can attack from any position on the battlefield. Generally, magic attacks also bypass armor to deal damage directly to health. The Silence ability reduces the magic attack of every card on the enemy team, and other abilities can alter the effectiveness of magic attacks (Void, Magic Reflect, Void Armor, Phase).
There are also cards with no attack but they make up for their lack of attack with other abilities.