Some scripted sequences are used to play short cut scenes that the player has little control of. However, they are commonly used in games such as Half-Life or Call of Duty to bring in new enemies or challenges to the player in a seemingly surprising manner while they are still playing. They can also present further plot points without requiring the player to take a break by watching a cut scene. The intended results of this style of presentation is to increase immersion and to maintain a smoothly-flowing experience that keeps the player's interest.
Scripted sequences trigger off of a number of things. A timer, progress of the game, or a check point could activate a scripted sequence. For players that speedrun video games, skipping these scripted sequences that would otherwise slow down their completion time is a talent. Being able to manipulate the games hit boxes so that the game does not trigger sequence is efficient for fast completions.