Many games are littered with non-critical dialogue and cutscenes. By "non-critical" I mean that it isn't necessary to watch or listen to in order to progress in the game or beat the game. Most of the dialogue and cutscenes that I have seen in games are there to shed more light on the story of the game. However, there are many players out there, including myself, that care very little about the story of the game and care more about the action of the game. I want to actually play the game and not be forced to listen to some scripted dialogue or scene for a couple minutes between characters in the game. That's why it's really nice when games offer the ability to either skip through or fast forward through the dialogue or cutscenes.
EXAMPLE #1: Infinity Blade Trilogy
The Infinity Blade Trilogy all allow the player to fast forward through any and all dialogue between characters. There are also brief cutscenes in the game when the player chooses one of the paths in front of the character. For example, the player may choose to battle an enemy. Before the fighting actually begins, there is a brief cutscene that shows the character and enemy approach each other and prepare for battle. All of this can be skipped by fast forwarding through it that way the player won't have to sit idly by and watch it.
EXAMPLE: Batman Arkham Knight
Batman Arkham Knight also allows the player to skip the cutscenes and jump directly into playing the game. In almost all the cutscenes player is asked to skip the cutscenes and player can skip them at any point of time if he isn't interested in following the story. In this way, momentum is not lost by the player who is more interested to experience the game through its gameplay rather than going through the cutscenes.
EXAMPLE: The Book of Unwritten Tales
The game offers to skip cutscenes by the click of your mouse. This makes it possible for the player to skip the story parts, and get to the puzzles faster. Not only the cut-scenes can be skipped, but dialog lines can be clicked through fast, in case you read the lines before the characters have finished their voice line. This makes it easy to get past the reading parts and get to the puzzles.