A multi-single speedrun is the concept of having two or more people compete with one another in a single player game instead of a single, split-screen, or multiplayer speedrun.
This is the basis behind the many speedruns seen in I'm A Speedrunner and similar tournaments and events in the SpyroSpeedruns community. There are a variety of these kinds of speedruns ranging from the most basic collect-a-thon to the more rare tag-team co-operative matches.
A multi-single speedrun is often done live either in the same room or more commonly over a VoIP program such as Skype and a proposed game and objective for the speedrun is decided upon in advance. Once an agreement is reached, the competitors prepare their recording software for both commentary and video footage of the game they're playing and in some cases game audio.
One competitor (or observer) will start a countdown to signify the start of the run and then race to complete their objective(s) before their opponents do. As the competitors aren't allowed to see anyone's screen except their own, they will often let everyone know where they're at during the race.
Once a match has finished, each competitor prepares their video for editing to be put into a single split-screen video. They are then given to the volunteer video editor. As the guidelines are rather loose, the editor can be however fancy they want but they must provide the following information either in the video or YouTube's video description: Game, Objective(s), Names of Competitors, etc. In the case of tournaments, the video must be uploaded before the deadline or risk being made Void.