What sense does it make not to drive or turn on the light on Shabbat?

In order to understand the laws pertaining to Shabbat, we must first understand the basis and underlying nature of the Day of Rest.

The reason we rest on Shabbat is because "It was during the six weekdays that G-d made the heaven, the earth, the sea and all that is in them, but he rested on Saturday. G-d therefore blessed the Sabbath day and made it holy (Exodus 20:11)."

Now, we must understand what the Torah means when it says that G-d "rested." Was He tired? How can an infinite, omnipotent G-d need to rest?

Besides, the Torah tells us that G-d created the entire universe by speaking. Did that exhaust G-d to the point that He needed to unwind?

The answer is very simple. G-d did not rest from exertion--he rested from creation.

Creation is not necessarily synonymous with exertion and physical effort.

On the seventh day, G-d rested from creating. On Shabbat, we too abstain from "creating."