A speedrun is a play-through, or recording thereof, of a whole video game or a selected part of it (such as a single level) performed with the intent of completing it as fast as possible, optionally under certain prerequisites, mainly for the purposes of entertainment and competition. The term is a compound of the words speed and run (as in "running" through a game, referring to the playing of a game). There's also a website for uploading recorded speedrun videos at http://www.speedrun.com/
Commonly, speedruns are recorded on either media such as DVDs (predominantly when games on consoles are concerned), or as digital files, by the people ("players") who make them, for entertainment, time refinement, or verifiability purposes.
Entertainment has traditionally been the reason for the creation of speedruns, as the phenomenon was originally devised by enthusiasts who began comparing each other's playing skills via movies exchanged over the Internet, while verifiability stems from the necessity to provide evidence that one's playthrough went by the typical or game-specific speedrun rules and thus counts as a valid attempt to beat the record.
In order to attain the highest possible quality of play in a speedrun, the author usually has to look at and think about the game differently from the way that most casual gamers would. It is usually required that speedruns be planned out carefully before they are attempted; this need stems from the complexity of the separate areas in which the gameplay takes place. Additionally, games and their physics engines are not flawless and will allow the runner to do unexpected things that could save time. Despite their inherent differences, they seem to share a lot of common traits in this context, such as the ability to disjunct the common sequence of events in a game and thus skip entire parts of it—the act of sequence breaking—and the ability to use programming errors, or glitches, to one's advantage.
Some games are considered to be ideal specimen for fast completion purposes and have online communities dedicated to them, which provide (or have provided) a highly active platform for discussing the speedrunning of one or more of these particular games.
While speedrunning initially started out as a small project, initiated by a few enthusiasts who shared their demos online, it has since become a phenomenon that encompasses several active websites and an increasingly expansive assortment of speedrun videos that are freely and widely circulated on the Internet.
Some games once you have enough speedrunning skill can probably be treated by a random walk for how far into the game you are after each amount of time. Suppose a game can be treated like a 1,000,000 step random walk starting from 0 and the speedrun can be divided up into 1,000,000 parts and every part has exactly 2 possible lengths of time that differ by the same amount and being faster in a part is considered moving up 1 in the random walk and being slower in a part is considered moving down 1. After 1,000,000 steps, the probability function with domain even numbers of where you end up is approximately given by e1/2,000,000 x2 times some constant. A normal distribution is any distribution that can be gotten from that one by stretching it along the x-axis by a positive amount, stretching it along the y-axis by the reciprocal of that amount, and moving it along the x-axis any amount. It can be proven that the standard deviation of the function e-1/2x2 is 1. If your current record corresponds to a 1,000,000 step random walk that ends at 20,000, then the expected number for your next record is 20,050. However, it is not worth resetting if you're at 9,500 after 500,000 steps. The math shows that given that a 1,000,000 step random walk ends at 20,000, the probability distribution of where you were half way through the random walk is normal with a standard deviation of 500. Although it's so much rarer to advance 10,500 steps in the second half than 10,000, it's also so much less rare to advance 9,500 steps in the first half than 10,000 that the probability of advancing 9,500 steps in the first half then 10,500 in the second half is only square root of e times less than the probability of advancing 10,000 steps in the first half and 10,000 in the second half. You're going to get way fewer chances to get to 10,000 in the first half than 9,500 so you might as well make do with the times you get to 9,500 in the first half and not reset the run.
Also, if you still have more skill to be gained, you will probably gain it faster if you do no reset runs because every time you reset after failing a trick and costing a lot of time, you miss your chance to get practice on all those later hard tricks and slow down your ability to gain experience from which you can figure out what to try and see what happens. Probably almost everybody can keep taking in new information and retaining it but at a very sluggish rate. If that turns out to be the case, one thing you could try is to learn how to write a formal proof in a weak system of pure number theory. You could try mentally figuring out proofs of statements and adding at a sluggish rate, adding them to the list of statements you have proven and retained and figuring out new statements from ones you recalled from the list and occasionally adding them to that list. You could also slowly add to your mental list statements about your past speedrunning experience and keep adding more statements some of which can be figured out from statements you previously figured out and some of which can be gotten by combining a new observation with a statement you previously added to your list.
An example of a good speedrun is a Super Mario Sunshine 100% speedrun found at https://www.youtube.com/watch?v=I41AB1Dqc14 linked by https://www.speedrun.com/sms#120_Shines. It was a hacked file. In both the hacked one and the unhacked one at https://www.youtube.com/watch?v=Oh88dv14xO0, the cutscene telling Mario to clean up all that ugliness ends at 6:47. The hacked one cuts out 5:40 so 5:40 is added on at file select. For those of you who want to check the accuracy of that claim, the YouTube video https://www.youtube.com/watch?v=d_hXy_XsPMo pretty much gives you proof. You may have trouble seeing what's going on in that video recording 2 videos so it's worth mentioning all YouTube videos now let you jump back 5 seconds by pressing the left arrow key. 2:21:45 into the speedrun, Paperario was 1:15 ahead. Yet, he only beat his personal best by 19 seconds. The math shows that it's normal to expect something like that from a good speedrunner. People who have confusion why a certain part of that speedrun went a certain way will probably end up happier when this page just won't give it away to them and leaves them to try and figure out themselves a possible reason. It can be done. Even if you don't want to speedrun, it may be fun for you studying that speedrun. You might also want to further study his general tendencies by watching him streaming Super Mario Sunshine 100% speedruns at https://www.twitch.tv/paperarioms if he's still streaming them or watching the person with second place streaming them. Super Mario Sunshine has enough competition to get really good speedruns in 100% so it's probably a good game to study 100% speedruns of.
In some games for 100%, you might need to adapt your route based on RNG from earlier in the game. For example if there are many bushes in the game and every time you erase your file, each one is random whether it has money in it and after you chop it, it never comes back. Some games like Majora's Mask keep track of the game time and have events that occur at certain times so for 100%, it's probably not worth picking a route that makes it so hard to do what you need to do fast enough to not miss the event because there probably is a way different but barely slower route that doesn't give such tight timing.