How do window blinds work?

Because of color or, more accurately, albedo and reflection.

Sunlight enters your room through your window, because your window is largely transparent. It hits your floor or other things in your room and gets absorbed or reflected inside your room. The amount of heat varies depending on location, where the sun is, how big your window is, but direct sunlight, filtered through a glass window, you're talking a couple hundred to a few hundred watts per square meter. If the window is 2 square meters, that's not as much as a space heater, but not too far off.

The blinds are in the room, but they are white and reflective, so much of the sunlight that comes into your room hits the blinds and bounces back out the window. If your floor is white, the sunlight hits the floor but gets reflected in all directions so it stays in the room. The blinds being close to the window reflect a considerable percentage of the heat carrying sunlight back out the window. Any white covering next to the window would do the same.

I heard a story/saw a photo once about a couple who custom built a house in Maine with huge windows to take advantage of natural solar energy in winter and they did it a little too well. The inside of their house would reach 90 degrees during winter.