The health bar is a visual indicator that shows how much life a unit has. Other visual effects may also be present on the bar. For champion health bars, the display name may also be changed while the unit is under certain states.
The Armor up, Magic Resistance up, and Resistances up only indicate a temporary increase in Armor, Magic Resistance, or both, respectively.
The Armor up, Magic Resistance up, and Resistances up will only have a visible icon if, after the champion gains the temporary bonuses, the following equation is true:
Sources that provide temporary resistances, and can display The Armor up, Magic Resistance up, or Resistances up icons, will be added together for the purposes of determining if the icon will be visible.