According to the ingame stats menu, Melee Defense is defined as:
"This is your ability to perceive and defend against attacks from opponents. By increasing this skill, you will block and evade more attacks when using a sword. You will also take less damage, and will be less likely to stumble when hit by a weaker attack. A balanced swordsman would keep this skill similar to his Melee Attack level."
Ways to increase Melee Defence quickly:
An effective yet high risk method of raising melee attack and defense quickly is by lowering your combat skills. This happens when you equip a backpack, Chainmail, various helms or some armours such as the Holy Chest Plate. In combat, when your stats show a negative in brackets (e.g -10 from a traders large backpack) this is the base used to calculate your experience gain. Meaning, if you have 20 defence normally and find it is levelling slowly, if you equip a traders large backpack it will be counted as 10. You will then gain the amount of exp that someone with 10 melee defence would. This is also true of Melee Attack.
Pieces of equipment that lower your combat abilities are cumulative, for example a large traders backpack in addition to chainmail, the holy chest plate and a tin can helmet would lower your skills by (-18).