Someone who is in the driver's seat is in control of something. Like a driver steers a car, they are steering a situation.
This expression actually dates back to the mid-1800s, before cars existed. Originally it referenced the driver in a horse-drawn carriage, who sat on the outside and directed the horses, and it was often used in politics. Nowadays, it's used more widely. For example, you might say that students are in the driver's seat of their education if they're taking an active role in learning. Or you might say a company is in the driver's seat if they're shaping the market.