Variable Neutral Density Filters
A neutral density filter blocks some of the light getting into a camera. A variable ND filter allows you to control the light limiting affect of the filter just by twisting one part of it. In effect they are made from two polarizing screens and each of these is like a venetian blind, so when one filter is overlaid against the other the light level is restricted. Variable ND filters uses the properties of polarized light, where the two parallel polarizing filters will block very little light but when the two are configured at 90 to each other will block nearly all light travelling through them. There are a range of these filters on the market and price and quality vary considerably.
Because the ND filter allows you to control the amount of light entering the camera it can augment the shutter and aperture controls . This lets you increase the exposure time and/or use a wider aperture while using the neutral density filter to prevent overexposure.
The main use with a neutral density filter are to get shallow depth of field (a wide aperture) or long motion blur (a long exposure) under bright lighting conditions. This makes it very handy for taking portraits or nature shots, where you have bright lighting but want a shallow depth of field, or capturing the feel of a public event while blurring out individual people as they move. Combined with low ISO and a small aperture, they can allow you to have long exposures of 30 seconds or more in bright sunlight.
This method Find out more about polarization, including in photography, here. This variable neutral density filter is far from perfect, but great if you want to make one cheaply!