Block is a defensive stat enabling you to stop damage from happening to your character.
Block is affected by the amount given by the base stance, how much additional is added as the stance progresses, agility and gear.
Agility affects block as a percentage of the amount granted by the stance. For every point of agility above 5 you gain 10% of the base stance amout. [Unconfirmed: every point below 5 should drop the amount by 10%.] If the stance grants a total of 10, then 8 agility (+3 over 5) will increase that by 30% to 13 before adding gear.
Generally the only gear with +block on it will be shields.
Block can protect your character against ranged physical attacks (guns, not magic) as well as melee attacks. [Unconfirmed: Block is not penalized by the number of simultaneous attackers engaged with you, as evasion apparently is.]