You stage a crime scene when you are close to a victim and you hope to direct the investigation away from you.
The most typical example in a murder case is a husband kills his wife, and wants to make it appear that she was killed in a burglary gone wrong.
They always screw this up, taking things that a burglar wouldn’t take, not taking things that he would, ransacking areas that wouldn’t typically be ransacked, opening drawers in a way that a burglar wouldn’t, etc.
They sometimes dump “stolen” items near the residence, as they don’t have time to get rid of them, or when they worry about having something that would tie them directly to a murder.
Staging a crime scene, almost always has the opposite effect of what one intends.