Why was The Gunpowder Plot a turning point in history?

It depends highly on which point of view you see it from.

On the one hand, people began to see that they had more power to control the government with force, which in turn lead to an influx of protests/riots when the people didn't like the decision of government, whereas previously they were more quiet/accepting of the government.

From the governments perfective however it showed that they should be more wary of the people and that they actually had a lot more power than they thought. The royal argument for this would've increased the laws regarding treason- making harsher punishments than previous.