A Yandere girl is a girl who loves a boy so much that she is willing to threaten, harm, or kill whoever interested in him. Yandere Simulator is a stealth game about stalking a boy and secretly eliminating anyone who seems interested in him, while maintaining the image of an innocent schoolgirl.
The gameplay is similar to the Hitman series; you are put into a large environment filled with many NPCs, and you must track down specific targets and eliminate them. You can use stealth to kill your target without any witnesses, stage an accident that leaves no evidence, or just slaughter anyone who gets in your way. If you don't dispose of corpses, clean up blood, and destroy evidence, then the police might be able to link you to a murder and arrest you.
If you don't want to get any blood on your hands, you can use social sabotage to get rid of a girl; frame her for one of your crimes, get her expelled from school, or ruin her reputation. If you truly want her to suffer, you could convince every other girl in school to bully her until she commits suicide and saves you the trouble.
If the boy you love witnesses you committing murder, he could never love you, and the game would be over.