Legendary Item Bad Luck Protection
When it comes to most targettable loot from a boss (gear/mounts/pets etc.) those drops have a fixed drop chance. If "Boots of Unending Awesomeness" have a 33% chance of dropping, that chance will always be 33% regardless of how many loot-eligible times you kill that boss.
Legendaries on the other hand, if you are running Legendary-eligible content and don't get a Legendary, then your chance of getting one with increase over time. The more content you do without getting a Legendary, the higher your chance will become.
Let's say you have 3-sided die. If you roll the number 3, you get the item.
In the case of the "Boots of Unending Awesomeness," you could roll the die 20 times and never get a 3. Your chance of getting a 3 on your next roll is still 33%, as all rolls are considered unique and do not take previous rolls into account; the die cares not for the fact that you've yet to roll a 3.*
(*note that this refers to the items that drop directly from the boss and not the system of winning items via bonus loot, which has its own logic.)
In the case of Legendaries, you could roll the die 20 times and never get a 3. However, with bad-luck protection, the die will become more and more weighted toward giving you a 3. Due to the die becoming more weighted, the chance of getting a 3 on your next roll will be higher than without bad luck protection.