A passive bonus is an ability that is always present, at least under certain circumstances. They are passive because they do not require the player to initiate them, in contrast to an activated ability.
Examples of passive bonuses include "Increases your dodge chance by 1%" and "After being struck by a melee or ranged critical hit, heal 8% of the damage taken over 6 seconds." In the first example, the ability is always present. In the second, a specific trigger is needed, but that trigger does not come from the player.
One could argue that even basic attribute bonuses on items are a passive bonus.