It's a simple stall tactic. If person A gets mad at person B and wants to shoot them they have to wait 7, 10, 14 days whatever before they can legally buy the fun from a dealer. Flawed logic though as guns are durable goods openly available immediately on the used market. Flawed logic again in that if someone plans to go after someone, they most likely aren't going to use a 400+ dollar gun that they have to wait a week for, they will ram them with the car, stab them with the kitchen knife, poison their food, etc, whatever is quicker, cheaper, and easier. The only way the stall tactic works is to prevent large scale attacks from an aggravated person....disgruntled employee or student typically....that goes to get a big gun to shoot up the place that "just ruined their life" but after a week they simmer down and don't go through with the plan. But again logic, even on that, is flawed because cars can go through walls, and bombs aren't hard to make with items readily available in stores, not to mention a gas can and a match.
The waiting period is designed to stop gun violence, and it does...it increases other types of violence, at least in theory.