Shield skill is agility based, you need 3 agility for each rank of shield skill you want to level up. Shield skill is the "difficulty" listed on the item page for each item.
When you successfully block with your shield, it takes damage instead of you. The hit points/armor listed are the shield's "life" and work the same way as a player's hit points.
Extra levels of shield skill beyond the required difficulty level will increase your speed and blocking radius, as well as increasing your shield's durability.