they will make light reflected off of things less bright.
polarization is the 'tilt' of light. think of light as a sine wave, but it can be tilted in any direction.
polarization allows only the component of the light that's in a specific direction to be passed through. remember dot product from Freshmen Physics or from Vector Calculus? polarization works like that.
For instance, if you have a polarizer with a horizontal transmission axis, it only lets the horizontal light through. if you have a horizontal wave, it all goes through. if you have a vertical wave, none of it goes through. if you have a wave of amplitude "A" and angle "theta", the amount of light passed through is Acos(theta). Since the light intensity is the square of the amplitude, you get I = Io * cos^2(theta), which is called Malus' Law, where I is the intensity of the light you see, Io is the initial intensity, and theta is the angle between the transmission axis and the polarization of the light.
Now, since natural light is polarized in all random directions (we can say 0 < theta < 2pi), we can find the average I of randomly polarized light.
I = Io/(2pi) multiplied by the integral from 0 to 2pi of cos^2(theta)
The result of this is that I = Io/2
That is to say, looking at randomly polarized light through a polarizer, half of the light passes through. this doesn't affect how you see objects, just the brightness.
but that's just for objects lit by randomly polarized natural light.
the fun part of a polarizer is when we get into coherent light. coherent light is all polarized exactly the same. usually it comes as a result of reflection off of a glossy surface, such as a car's paint, or water, or something like that.
now, we go back to Malus law. If the transmission axis is perpendicular to the coherence axis, none of the light will go through!!!
the effect of this is that if you have coherent light reflected off of a television, or a car, or a lake, polarized sunglasses will remove that light, while keeping the rest of the light.
now, the one issue is that you may have trouble viewing certain things. For instance, i used to have polarized sunglasses, and if I had to use my cell phone, i needed to take them off, because the polarization blocked all the light coming from the phone's screen.
