Teeing up on the correct side of the teeing ground promotes a better angle to your target—and a safer shot. I always recommend to slicers that they tee up on the far right side. Then they will naturally aim left and shoot back across the tee. The ball will have more room to curve from left to right. Hitting from the right side also helps if the wind is blowing from left to right.
Conversely, teeing up on the left side encourages you to aim right. That helps if your basic shot is a right-to-left draw, or if the wind is blowing from right to left. I will go so far as to stand outside the left tee marker when there is a strong right-to-left wind (with my ball inside the marker), to tee up as far left as possible and give myself a better line.
Another factor to consider is the hole location. On this par 3, a hazard cuts into the right side of the green. I want to enter the green to the left of the yellow stake that is left of the flagstick. I am not aiming at the flagstick, because that’s too risky. Teeing up on the right side of the teeing ground gives me the best angle to reach my target area.