Tanking is a term that refers to surviving a 1-hit kill shot (usually from a sniper such as the L96A1, or the L115A2/A3) by reducing the damage output of the weapon (a side effect of extreme range) or by mitigating the damage received by the target (usually by wearing body armor).
Tanking due to range happens when the target is at the maximum range of the weapon. The damage output of all firearms is reduced gradually over its effective range, to zero beyond its maximum range. Tanking of this sort occurs on maps such as Kill Creek, due to the distance between spawn points. In another large map like Costa Recon, the opposite edges of the map are beyond maximum range of most sniper rifles, causing shots at this range to be tankable.
Many vests can contribute to tanking. The Heavy Vest is commonly used for this purpose; it is unlocked at the rank of Corporal. The Balanced Vest, another GP gear item, is slightly inferior to the Heavy Vest in protection, but has a slightly lower speed penalty. Both vests have a greater chance of tanking than lighter vests. The first available NX vest is the Assault Vest, an upgraded Balanced Vest with the same protection but a speed increase, which can also contribute to tanking. The Tanker Vest is the NX counterpart of the Heavy Vest, with a smaller speed penalty and slightly better protection. Another good tanking vest is only available with Hauser: the Commando Vest is the strongest vest in terms of damage absorption. More information can be found on this page.
Bad aim or poor shot placement on the target's body can contribute to tanking. If a 1-hit kill sniper rifle hits the target in the lower leg or foot, the shot will most likely not kill them even if the shot was taken at close range, even if the target is wearing light armor like a Light Vest or Recon Vest.