In computer and video games a play through is a specific instance of playing a game, presumably from beginning to end. Let's say that you start a game of Super Mario 64, get seventy stars, then forget about it. Years later you pull out the cartridge and start a second game which you play until you beat Bowser and save Princess Peach. You completed the second play through but not the first. Since most games have linear plots and some element of choice the notion of "my play through" is important to understanding the psychological attachment to a game. When you play through Doom there are opportunities to pick up weapons early, secrets to find, and alternate routes which mean that every person's play through contains a string of failures, triumphs, and trade offs that make it uniquely theirs. This collection of actions and consequences mean that if you play somebody else's saved game it has no causal or emotional connection to what you did. In a game with as little in the way of plot as Doom this is mostly inconsequential.
In a game like Fallout New Vegas it is enormously important. New Vegas has four endings each of which has it's pros and cons. Will you side with the fascist but effective Caesar's Legion, the corrupt but democratic NCR, the competent Autocrat Mister House, or will you create a free and independent New Vegas. It is literally your choice and that's barely scratching the surface when it comes to decisions you're presented with. Holding to any sort of moral code will be fraught and behaving like a murder hobo will be hollow. More than any other game that I can think of New Vegas teaches you about your moral preferences in a messy and uncertain world. In this sense play throughs can be deeply personal affairs where you explore what it would be like to be a true hero or villain. While New Vegas may be the best it's hardly the only game to deploy moral dilemmas. Undertale lets you spare every foe, Bioshock has the little sisters, and even Half-Life lets the player kill security guards for ammo or not. These elements give players a sense of agency greater than mere success or failure and means that separate play throughs can be very different experiences.
If somebody where making a taxonomy of peoples' interaction with electronic games play through would be at the top level. Below it would be sessions and below that individual encounters. That said, some games like Age of Empires are structured such that the notion of a play through is muddy. Age of Empires has random maps and scenarios. Neither the random maps nor the individual scenario maps provide any meaningful continuity with each other. A pyrrhic victory is the same as totally crushing your foes from the perspective of the next level. More over there is no clear end. Beating all of the scenarios is just that. Random maps are purely pass/fail affairs which contribute to a wins/loses count. In this sense there is no clear delineation for a play through. Many games for go these and in that sense have no end and one's play through ends when they quit for the last time. Exceptions withstanding, for most players in most games the play through is the game. We play until the credits roll (assuming we even finish the game) and then we're done. Play through as a conceptual unit is extremely useful if not down right essential for discussing what a game is and so I expect this term to endure for as long as computer and video games do.
IRON NODER XV: LAST SECOND BARE BONES IRON NODER FREAKOUT!