According to Wikipedia the use of the word "Tanking" to describe a unit or team's ability to absorb damage originated in the text based Multi User DUngeons (MUDS) of the 1990s. The concept probably reached its full potential in the Tank, Heal, Damage triumvirate of massively multi player games such as Everquest. With classes specialised in each of these roles player groups can work together to overcome PVE monsters (Raid Bosses) that are enormously more powerful than themselves. The tanking classes have special skills to keep monsters focus upon themselves and then rely on heavy armour and defensive abilities to reduce the damage sustained to a level that the healers can heal. Knowing that "the tank is holding" means that your combination of mitigation and healing is sufficient to survive the incoming damage and is a vital first step to victory.
The terminology is widely used in role playing games and real time strategy games but the principle can be applied to just about any game against computer opponents (PVE) even when the phrase "tanking" isn't commonly used. In a shooter for example once you have found a reliable piece of cover to crouch behind you are able to survive incoming fire (your tank is holding) and you can now focus on picking off opponents.
The concept of tanking is not as useful in PVP games because human players can change their tactics at will. Once it becomes obvious that they are failing to make a dent in your defences a human player is likely to try a different approach. It would be foolish to think that you have won the battle just because "your tank is holding" against one line of attack.Nevertheless the ability to survive incoming attacks is important and tanking still essential. EVE online for example uses the term "tanking" extensively to describe the defensive capability of both individual ships and of fleets in PVE and PVP online space battles. One of my favourite depictions of of "The tank is holding" comes from EVE in the Clarion Call 3 video from Rooks and Kings
The entire video is worth watching but the particularly relevant bit starts at minute 29:00. A small fleet of specialised spacecraft is taking on a much larger and in theory more powerful fleet in the opponent's home territory. The upstart intruders are using superbly co-ordinated tactics to minimise incoming damage to a level that they can repair while they whittle down the opponent fleet. In short their strategy relies on their tank holding. The vital sequence starting at minute 29:00 begins with an expletive from the pilot of their repair ship (carrier) because one of the armour repair units (reppers) that is keeping him alive burns out through over use. You can hear the despair in his voice when he tells his team what has happened. There is a short dreadful pause as it dawns on everyone that the battle is surely lost but that thought is interrupted by the explosion in the background of one of the enemies main damage dealing ships (a Moros dreadnought). Then we get the deadpan reply of the fleet commander:
"It doesn't matter. One Moros is dead. The other one is held zero cap" (This means its guns are neutered and cannot fire).
"You can tank all their faction battle-ships on one repper".