It isn't entirely clear from the tooltip, but the shield's absorption capacity is determined by the target's current armor when 'hit' by the extender -- repairing the target does nothing to the shield. Whenever any ally inside the shield would take damage (even if the damage originates from inside the shield), reduce the damage by the indicated percentage; anything not hitting the ally is deducted from the shield's absorption, and when the shield hits its limit it ends. Thus, the shield lasts longest when it covers a single, heavily-armored target in full repair; hitting a damaged target or shielding a group shortens its lifespan, and the shield collapses after a single hit if cast on an unarmored target (such as a Turret).
Targeting another player, pet, or NPC when using this skill applies the shield to your target. This is ideal for escort missions, provided the subject you're escorting has a respectable armor rating.
Using the skill without a target applies the shield to your own armor. This dramatically improves your staying power when soloing. Given the high armor rating of Mech armor, unless a Commando is in the squad, you will often be the best target for the extender.
The individual "wearing" the shield can see it by zooming out, and will see an indicator in the status effects list below their health and armor and a colored glow around their feet. Other players will see the shield as a bubble around the player similar to the one around shield drones. The glow is visually distinct from the damage-reflecting drone -- you can visually tell whether a shielded target will merely reduce your damage or reflect it back at you.
The damage reduction from Shield Extender stacks with other sources of damage reduction, such as Base Wave. It is unclear if other damage reduction sources factor in to the maximum damage absorbed by the shield, or if the reduced damage also reduces the effectiveness of redirect effects like Reflective armor.
"The sapper uses micromech to form a shield around the target of this ability. The shield will emanate from the target, and will protect everyone in it by reducing incoming damage by a percentage determined by the ability pump level. The ability pump level and armor quality of the target are used to determine the total amount of damage mitigated by the shield."