Damage is the loss of HP to a mob or player. Damage can occur in many ways; ranging from the player hitting a mob, to a player falling into lava or off a cliff, to additional effect damage from a weapon, even Scorpion poison.
When a mob is inflicted with damage, it's health bar will decrease. When any health bar empties (any entity with a health bar is subject to this), the entity it is attached to will die, and drop it's loot (in the case of the player, nothing). Defence is a modifier that allows damage inflicted to be reduced.
When a mob makes contact with the player, or a spell makes contact with the player, or the player attacks another player or a mob, damage is dealt. Damage that is dealt can be amplified through certain ways;
Melee; Having a weapon with a certain damage range, and Strength.
Magic; Having a wand with a certain damage range, and Intellegence.
ARROWS; Having a bow with a certain damage range, and Dexterity.A critical hit will also inflict extra damage; usually about double the regular damage that would have been dealt from a single hit. Dexterity influences whether a critical hit is landed; more dexterity, more critical hits.